Aarti Singh

Anirudh Vemula, Yuda Song, Aarti Singh et al. · cmu

We propose a novel approach to addressing two fundamental challenges in Model-based Reinforcement Learning (MBRL): the computational expense of repeatedly finding a good policy in the learned model, and the objective mismatch between model fitting and policy computation. Our "lazy" method leverages a novel unified objective, Performance Difference via Advantage in Model, to capture the performance difference between the learned policy and expert policy under the true dynamics. This objective demonstrates that optimizing the expected policy advantage in the learned model under an exploration distribution is sufficient for policy computation, resulting in a significant boost in computational efficiency compared to traditional planning methods. Additionally, the unified objective uses a value moment matching term for model fitting, which is aligned with the model's usage during policy computation. We present two no-regret algorithms to optimize the proposed objective, and demonstrate their statistical and computational gains compared to existing MBRL methods through simulated benchmarks.

Eric Luxenberg, Dhruv Malik, Yuanzhi Li et al. · stanford

We consider robust empirical risk minimization (ERM), where model parameters are chosen to minimize the worst-case empirical loss when each data point varies over a given convex uncertainty set. In some simple cases, such problems can be expressed in an analytical form. In general the problem can be made tractable via dualization, which turns a min-max problem into a min-min problem. Dualization requires expertise and is tedious and error-prone. We demonstrate how CVXPY can be used to automate this dualization procedure in a user-friendly manner. Our framework allows practitioners to specify and solve robust ERM problems with a general class of convex losses, capturing many standard regression and classification problems. Users can easily specify any complex uncertainty set that is representable via disciplined convex programming (DCP) constraints.

Jennifer Hsia, Danish Pruthi, Aarti Singh et al. · cmu

Despite the rising popularity of saliency-based explanations, the research community remains at an impasse, facing doubts concerning their purpose, efficacy, and tendency to contradict each other. Seeking to unite the community's efforts around common goals, several recent works have proposed evaluation metrics. In this paper, we critically examine two sets of metrics: the ERASER metrics (comprehensiveness and sufficiency) and the EVAL-X metrics, focusing our inquiry on natural language processing. First, we show that we can inflate a model's comprehensiveness and sufficiency scores dramatically without altering its predictions or explanations on in-distribution test inputs. Our strategy exploits the tendency for extracted explanations and their complements to be "out-of-support" relative to each other and in-distribution inputs. Next, we demonstrate that the EVAL-X metrics can be inflated arbitrarily by a simple method that encodes the label, even though EVAL-X is precisely motivated to address such exploits. Our results raise doubts about the ability of current metrics to guide explainability research, underscoring the need for a broader reassessment of what precisely these metrics are intended to capture.

Shivani Chiranjeevi, Mojdeh Sadaati, Zi K Deng et al.

Insect-pests significantly impact global agricultural productivity and quality. Effective management involves identifying the full insect community, including beneficial insects and harmful pests, to develop and implement integrated pest management strategies. Automated identification of insects under real-world conditions presents several challenges, including differentiating similar-looking species, intra-species dissimilarity and inter-species similarity, several life cycle stages, camouflage, diverse imaging conditions, and variability in insect orientation. A deep-learning model, InsectNet, is proposed to address these challenges. InsectNet is endowed with five key features: (a) utilization of a large dataset of insect images collected through citizen science; (b) label-free self-supervised learning for large models; (c) improving prediction accuracy for species with a small sample size; (d) enhancing model trustworthiness; and (e) democratizing access through streamlined MLOps. This approach allows accurate identification (>96% accuracy) of over 2500 insect species, including pollinator (e.g., butterflies, bees), parasitoid (e.g., some wasps and flies), predator species (e.g., lady beetles, mantises, dragonflies) and harmful pest species (e.g., armyworms, cutworms, grasshoppers, stink bugs). InsectNet can identify invasive species, provide fine-grained insect species identification, and work effectively in challenging backgrounds. It also can abstain from making predictions when uncertain, facilitating seamless human intervention and making it a practical and trustworthy tool. InsectNet can guide citizen science data collection, especially for invasive species where early detection is crucial. Similar approaches may transform other agricultural challenges like disease detection and underscore the importance of data collection, particularly through citizen science efforts..

Yuda Song, Lili Chen, Fahim Tajwar et al.

The success of RL for LLM post-training stems from an unreasonably uninformative source: a single bit of information per rollout as binary reward or preference label. At the other extreme, distillation offers dense supervision but requires demonstrations, which are costly and difficult to scale. We study text feedback as an intermediate signal: richer than scalar rewards, yet cheaper than complete demonstrations. Textual feedback is a natural mode of human interaction and is already abundant in many real-world settings, where users, annotators, and automated judges routinely critique LLM outputs. Towards leveraging text feedback at scale, we formalize a multi-turn RL setup, RL from Text Feedback (RLTF), where text feedback is available during training but not at inference. Therefore, models must learn to internalize the feedback in order to improve their test-time single-turn performance. To do this, we propose two methods: Self Distillation (RLTF-SD), which trains the single-turn policy to match its own feedback-conditioned second-turn generations; and Feedback Modeling (RLTF-FM), which predicts the feedback as an auxiliary objective. We provide theoretical analysis on both methods, and empirically evaluate on reasoning puzzles, competition math, and creative writing tasks. Our results show that both methods consistently outperform strong baselines across benchmarks, highlighting the potential of RL with an additional source of rich supervision at scale.

Yusha Liu, Aarti Singh

In continuum-armed bandit problems where the underlying function resides in a reproducing kernel Hilbert space (RKHS), namely, the kernelised bandit problems, an important open problem remains of how well learning algorithms can adapt if the regularity of the associated kernel function is unknown. In this work, we study adaptivity to the regularity of translation-invariant kernels, which is characterized by the decay rate of the Fourier transformation of the kernel, in the bandit setting. We derive an adaptivity lower bound, proving that it is impossible to simultaneously achieve optimal cumulative regret in a pair of RKHSs with different regularities. To verify the tightness of this lower bound, we show that an existing bandit model selection algorithm applied with minimax non-adaptive kernelised bandit algorithms matches the lower bound in dependence of $T$, the total number of steps, except for log factors. By filling in the regret bounds for adaptivity between RKHSs, we connect the statistical difficulty for adaptivity in continuum-armed bandits in three fundamental types of function spaces: RKHS, Sobolev space, and Hölder space.

Yu Huang, Zixin Wen, Aarti Singh et al.

The ability to reason lies at the core of artificial intelligence (AI), and challenging problems usually call for deeper and longer reasoning to tackle. A crucial question about AI reasoning is whether models can extrapolate learned reasoning patterns to solve harder tasks with longer chain-of-thought (CoT). In this work, we present a theoretical analysis of transformers learning on synthetic state-tracking tasks with gradient descent. We mathematically prove how the algebraic structure of state-tracking problems governs the degree of extrapolation of the learned CoT. Specifically, our theory characterizes the length generalization of transformers through the mechanism of attention concentration, linking the retrieval robustness of the attention layer to the state-tracking task structure of long-context reasoning. Moreover, for transformers with limited reasoning length, we prove that a recursive self-training scheme can progressively extend the range of solvable problem lengths. To our knowledge, we provide the first optimization guarantee that constant-depth transformers provably learn $\mathsf{NC}^1$-complete problems with CoT, significantly going beyond prior art confined in $\mathsf{TC}^0$, unless the widely held conjecture $\mathsf{TC}^0 \neq \mathsf{NC}^1$ fails. Finally, we present a broad set of experiments supporting our theoretical results, confirming the length generalization behaviors and the mechanism of attention concentration.

Smriti Jha, Vidhi Jain, Jianyu Xu et al.

The ability to provide trustworthy maternal health information using phone-based chatbots can have a significant impact, particularly in low-resource settings where users have low health literacy and limited access to care. However, deploying such systems is technically challenging: user queries are short, underspecified, and code-mixed across languages, answers require regional context-specific grounding, and partial or missing symptom context makes safe routing decisions difficult. We present a chatbot for maternal health in India developed through a partnership between academic researchers, a health tech company, a public health nonprofit, and a hospital. The system combines (1) stage-aware triage, routing high-risk queries to expert templates, (2) hybrid retrieval over curated maternal/newborn guidelines, and (3) evidence-conditioned generation from an LLM. Our core contribution is an evaluation workflow for high-stakes deployment under limited expert supervision. Targeting both component-level and end-to-end testing, we introduce: (i) a labeled triage benchmark (N=150) achieving 86.7% emergency recall, explicitly reporting the missed-emergency vs. over-escalation trade-off; (ii) a synthetic multi-evidence retrieval benchmark (N=100) with chunk-level evidence labels; (iii) LLM-as-judge comparison on real queries (N=781) using clinician-codesigned criteria; and (iv) expert validation. Our findings show that trustworthy medical assistants in multilingual, noisy settings require defense-in-depth design paired with multi-method evaluation, rather than any single model and evaluation method choice.

Youngseog Chung, Dhruv Malik, Jeff Schneider et al.

The traditional viewpoint on Sparse Mixture of Experts (MoE) models is that instead of training a single large expert, which is computationally expensive, we can train many small experts. The hope is that if the total parameter count of the small experts equals that of the singular large expert, then we retain the representation power of the large expert while gaining computational tractability and promoting expert specialization. The recently introduced Soft MoE replaces the Sparse MoE's discrete routing mechanism with a differentiable gating function that smoothly mixes tokens. While this smooth gating function successfully mitigates the various training instabilities associated with Sparse MoE, it is unclear whether it induces implicit biases that affect Soft MoE's representation power or potential for expert specialization. We prove that Soft MoE with a single arbitrarily powerful expert cannot represent simple convex functions. This justifies that Soft MoE's success cannot be explained by the traditional viewpoint of many small experts collectively mimicking the representation power of a single large expert, and that multiple experts are actually necessary to achieve good representation power (even for a fixed total parameter count). Continuing along this line of investigation, we introduce a notion of expert specialization for Soft MoE, and while varying the number of experts yet fixing the total parameter count, we consider the following (computationally intractable) task. Given any input, how can we discover the expert subset that is specialized to predict this input's label? We empirically show that when there are many small experts, the architecture is implicitly biased in a fashion that allows us to efficiently approximate the specialized expert subset. Our method can be easily implemented to potentially reduce computation during inference.

Dhruv Malik, Yuanzhi Li, Aarti Singh

Policy regret is a well established notion of measuring the performance of an online learning algorithm against an adaptive adversary. We study restrictions on the adversary that enable efficient minimization of the \emph{complete policy regret}, which is the strongest possible version of policy regret. We identify a gap in the current theoretical understanding of what sorts of restrictions permit tractability in this challenging setting. To resolve this gap, we consider a generalization of the stochastic multi armed bandit, which we call the \emph{tallying bandit}. This is an online learning setting with an $m$-memory bounded adversary, where the average loss for playing an action is an unknown function of the number (or tally) of times that the action was played in the last $m$ timesteps. For tallying bandit problems with $K$ actions and time horizon $T$, we provide an algorithm that w.h.p achieves a complete policy regret guarantee of $\tilde{\mathcal{O}}(mK\sqrt{T})$, where the $\tilde{\mathcal{O}}$ notation hides only logarithmic factors. We additionally prove an $\tildeΩ(\sqrt{m K T})$ lower bound on the expected complete policy regret of any tallying bandit algorithm, demonstrating the near optimality of our method.

Vaibhav Jindal, Albert Liang, Aarti Singh et al.

Finding the initial conditions that led to the current state of the universe is challenging because it involves searching over an intractable input space of initial conditions, along with modeling their evolution via tools such as N-body simulations which are computationally expensive. Recently, deep learning has emerged as a surrogate for N-body simulations by directly learning the mapping between the linear input of an N-body simulation and the final nonlinear output from the simulation, significantly accelerating the forward modeling. However, this still does not reduce the search space for initial conditions. In this work, we pioneer the use of a deterministic convolutional neural network for learning the reverse mapping and show that it accurately recovers the initial linear displacement field over a wide range of scales ($<1$-$2\%$ error up to nearly $k\simeq0.8$-$0.9 \text{ Mpc}^{-1}h$), despite the one-to-many mapping of the inverse problem (due to the divergent backward trajectories at smaller scales). Specifically, we train a V-Net architecture, which outputs the linear displacement of an N-body simulation, given the nonlinear displacement at redshift $z=0$ and the cosmological parameters. The results of our method suggest that a simple deterministic neural network is sufficient for accurately approximating the initial linear states, potentially obviating the need for the more complex and computationally demanding backward modeling methods that were recently proposed.

Yu Huang, Zixin Wen, Yuejie Chi et al.

Reinforcement learning with verifiable rewards (RLVR) has been a main driver of recent breakthroughs in large reasoning models. Yet it remains a mystery how rewards based solely on final outcomes can help overcome the long-horizon barrier to extended reasoning. To understand this, we develop a theory of the training dynamics of RL for transformers on compositional reasoning tasks. Our theory characterizes how the effectiveness of RLVR is governed by the smoothness of the difficulty spectrum. When data contains abrupt discontinuities in difficulty, learning undergoes grokking-type phase transitions, producing prolonged plateaus before progress recurs. In contrast, a smooth difficulty spectrum leads to a relay effect: persistent gradient signals on easier problems elevate the model's capabilities to the point where harder ones become tractable, resulting in steady and continuous improvement. Our theory explains how RLVR can improve performance at the edge of competence, and suggests that appropriately designed data mixtures can yield scalable gains. As a technical contribution, our analysis develops and adapts tools from Fourier analysis on finite groups to our setting. We validate the predicted mechanisms empirically via synthetic experiments.

Zixin Wen, Yifu Cai, Kyle Lee et al.

Visual design is an essential application of state-of-the-art multi-modal AI systems. Improving these systems requires high-quality vision-language data at scale. Despite the abundance of internet image and text data, knowledge-rich and well-aligned image-text pairs are rare. In this paper, we present a scalable diagram generation pipeline built with our agent, Feynman. To create diagrams, Feynman first enumerates domain-specific knowledge components (''ideas'') and performs code planning based on the ideas. Given the plan, Feynman translates ideas into simple declarative programs and iterates to receives feedback and visually refine diagrams. Finally, the declarative programs are rendered by the Penrose diagramming system. The optimization-based rendering of Penrose preserves the visual semantics while injecting fresh randomness into the layout, thereby producing diagrams with visual consistency and diversity. As a result, Feynman can author diagrams along with grounded captions with very little cost and time. Using Feynman, we synthesized a dataset with more than 100k well-aligned diagram-caption pairs. We also curate a visual-language benchmark, Diagramma, from freshly generated data. Diagramma can be used for evaluating the visual reasoning capabilities of vision-language models. We plan to release the dataset, benchmark, and the full agent pipeline as an open-source project.

Nuoya Xiong, Aarti Singh

Reinforcement Learning with Human Feedback (RLHF) is a widely used fine-tuning approach that aligns machine learning model, particularly Language Model (LM) with human preferences. There are typically multiple objectives driving the preference, hence humans find it easier to express per-objective comparisons rather than a global preference between two choices. Multi-Objective RLHF (MORLHF) aims to use per-objective preference feedback and achieve Pareto optimality among these objectives by aggregating them into a single unified objective for optimization. However, nearly all prior works rely on linear aggregation, which rules out policies that favor specific objectives such as the worst one. The only existing approach using non-linear aggregation is computationally expensive due to its reward-based nature and the need for retraining whenever the aggregation parameters change. In this work, we address this limitation by transforming the non-linear aggregation maximization problem into a series of sub-problems. Each sub-problem involves only linear aggregation, making it computationally efficient to solve. We further extend our framework to handle multi-group scenarios, where each group has distinct weights for the objectives. Our method enables achieving consensus or maximizing the aggregated objective across all groups. Theoretically, we demonstrate that our algorithmic framework achieves sublinear regret and can be easily adapted to a reward-free algorithm. Empirically, leveraging our theoretical insights, we propose a nearly training-free algorithm once the optimal policies for individual objectives are obtained.

Ojash Neopane, Aaditya Ramdas, Aarti Singh

Estimation and inference for the Average Treatment Effect (ATE) is a cornerstone of causal inference and often serves as the foundation for developing procedures for more complicated settings. Although traditionally analyzed in a batch setting, recent advances in martingale theory have paved the way for adaptive methods that can enhance the power of downstream inference. Despite these advances, progress in understanding and developing adaptive algorithms remains in its early stages. Existing work either focus on asymptotic analyses that overlook exploration-exploitation tradeoffs relevant in finite-sample regimes or rely on simpler but suboptimal estimators. In this work, we address these limitations by studying adaptive sampling procedures that take advantage of the asymptotically optimal Augmented Inverse Probability Weighting (AIPW) estimator. Our analysis uncovers challenges obscured by asymptotic approaches and introduces a novel algorithmic design principle reminiscent of optimism in multiarmed bandits. This principled approach enables our algorithm to achieve significant theoretical and empirical gains compared to prior methods. Our findings mark a step forward in advancing adaptive causal inference methods in theory and practice.

Ojash Neopane, Aaditya Ramdas, Aarti Singh

Estimation of the Average Treatment Effect (ATE) is a core problem in causal inference with strong connections to Off-Policy Evaluation in Reinforcement Learning. This paper considers the problem of adaptively selecting the treatment allocation probability in order to improve estimation of the ATE. The majority of prior work on adaptive ATE estimation focus on asymptotic guarantees, and in turn overlooks important practical considerations such as the difficulty of learning the optimal treatment allocation as well as hyper-parameter selection. Existing non-asymptotic methods are limited by poor empirical performance and exponential scaling of the Neyman regret with respect to problem parameters. In order to address these gaps, we propose and analyze the Clipped Second Moment Tracking (ClipSMT) algorithm, a variant of an existing algorithm with strong asymptotic optimality guarantees, and provide finite sample bounds on its Neyman regret. Our analysis shows that ClipSMT achieves exponential improvements in Neyman regret on two fronts: improving the dependence on $T$ from $O(\sqrt{T})$ to $O(\log T)$, as well as reducing the exponential dependence on problem parameters to a polynomial dependence. Finally, we conclude with simulations which show the marked improvement of ClipSMT over existing approaches.

Kanad Pardeshi, Samsara Foubert, Aarti Singh

In many real-world settings, a centralized decision-maker must repeatedly allocate finite resources to a population over multiple time steps. Individuals who receive a resource derive some stochastic utility; to characterize the population-level effects of an allocation, the expected individual utilities are then aggregated using a social welfare function (SWF). We formalize this setting and present a general confidence sequence framework for SWF-based online learning and inference, valid for any monotonic, concave, and Lipschitz-continuous SWF. Our key insight is that monotonicity alone suffices to lift confidence sequences from individual utilities to anytime-valid bounds on optimal welfare. Building on this foundation, we propose SWF-UCB, a SWF-agnostic online learning algorithm that achieves near-optimal $\tilde{O}(n+\sqrt{nkT})$ regret (for $k$ resources distributed among $n$ individuals at each of $T$ time steps). We instantiate our framework on three normatively distinct SWF families: Weighted Power Mean, Kolm, and Gini, providing bespoke oracle algorithms for each. Experiments confirm $\sqrt{T}$ scaling and reveal rich interactions between $k$ and SWF parameters. This framework naturally supports inference applications such as sequential hypothesis testing, optimal stopping, and policy evaluation.

Deming Chen, Jason Cong, Azalia Mirhoseini et al.

Artificial intelligence (AI) and hardware (HW) are advancing at unprecedented rates, yet their trajectories have become inseparably intertwined. The global research community lacks a cohesive, long-term vision to strategically coordinate the development of AI and HW. This fragmentation constrains progress toward holistic, sustainable, and adaptive AI systems capable of learning, reasoning, and operating efficiently across cloud, edge, and physical environments. The future of AI depends not only on scaling intelligence, but on scaling efficiency, achieving exponential gains in intelligence per joule, rather than unbounded compute consumption. Addressing this grand challenge requires rethinking the entire computing stack. This vision paper lays out a 10-year roadmap for AI+HW co-design and co-development, spanning algorithms, architectures, systems, and sustainability. We articulate key insights that redefine scaling around energy efficiency, system-level integration, and cross-layer optimization. We identify key challenges and opportunities, candidly assess potential obstacles and pitfalls, and propose integrated solutions grounded in algorithmic innovation, hardware advances, and software abstraction. Looking ahead, we define what success means in 10 years: achieving a 1000x improvement in efficiency for AI training and inference; enabling energy-aware, self-optimizing systems that seamlessly span cloud, edge, and physical AI; democratizing access to advanced AI infrastructure; and embedding human-centric principles into the design of intelligent systems. Finally, we outline concrete action items for academia, industry, government, and the broader community, calling for coordinated national initiatives, shared infrastructure, workforce development, cross-agency collaboration, and sustained public-private partnerships to ensure that AI+HW co-design becomes a unifying long-term mission.

Kanad Pardeshi, Bryan Wilder, Aarti Singh

Online learning algorithms continually update their models as data arrive, making it essential to accurately estimate the expected loss at the current time step. The prequential method is an effective estimation approach which can be practically deployed in various ways. However, theoretical guarantees have previously been established under strong conditions on the algorithm, and practical algorithms have hyperparameters which require careful tuning. We introduce OEUVRE, an estimator that evaluates each incoming sample on the function learned at the current and previous time steps, recursively updating the loss estimate in constant time and memory. We use algorithmic stability, a property satisfied by many popular online learners, for optimal updates and prove consistency, convergence rates, and concentration bounds for our estimator. We design a method to adaptively tune OEUVRE's hyperparameters and test it across diverse online and stochastic tasks. We observe that OEUVRE matches or outperforms other estimators even when their hyperparameters are tuned with oracle access to ground truth.

Grace Liu, Yuxiao Qu, Jeff Schneider et al.

Many tasks require learned models to strategically gather relevant information over multiple rounds of interaction before actually acting on a task. Strategic information gathering requires models to know not only how to effectively acquire information, but also when to stop gathering information and make a decision, in order to avoid overthinking or getting derailed when acting. In this paper, we formalize this problem and introduce Counterfactuals and Reasoning for Termination (CaRT), an approach for teaching LLMs when to stop seeking information. To appropriately learn when to terminate, CaRT fine-tunes LLMs using counterfactual pairs of trajectories, one where termination is appropriate and a minimally modified version of the same trajectory where it is not. It trains the LLM to explain the rationale for the termination decision in either case via verbal reasoning, and imbues this capability into the base LLM via fine-tuning. We instantiate CaRT in two domains: interactive medical diagnosis and math problem solving. In both domains, we find that CaRT improves the efficiency of information gathering and task success rate compared to other fine-tuning methods.

Yuda Song, Dhruv Rohatgi, Aarti Singh et al. · cmu

Partial observability is a notorious challenge in reinforcement learning (RL), due to the need to learn complex, history-dependent policies. Recent empirical successes have used privileged expert distillation--which leverages availability of latent state information during training (e.g., from a simulator) to learn and imitate the optimal latent, Markovian policy--to disentangle the task of "learning to see" from "learning to act". While expert distillation is more computationally efficient than RL without latent state information, it also has well-documented failure modes. In this paper--through a simple but instructive theoretical model called the perturbed Block MDP, and controlled experiments on challenging simulated locomotion tasks--we investigate the algorithmic trade-off between privileged expert distillation and standard RL without privileged information. Our main findings are: (1) The trade-off empirically hinges on the stochasticity of the latent dynamics, as theoretically predicted by contrasting approximate decodability with belief contraction in the perturbed Block MDP; and (2) The optimal latent policy is not always the best latent policy to distill. Our results suggest new guidelines for effectively exploiting privileged information, potentially advancing the efficiency of policy learning across many practical partially observable domains.

Jianyu Xu, Vidhi Jain, Bryan Wilder et al.

With advances in generative AI, decision-making agents can now dynamically create new actions during online learning, but action generation typically incurs costs that must be balanced against potential benefits. We study an online learning problem where an agent can generate new actions at any time step by paying a one-time cost, with these actions becoming permanently available for future use. The challenge lies in learning the optimal sequence of two-fold decisions: which action to take and when to generate new ones, further complicated by the triangular tradeoffs among exploitation, exploration and $\textit{creation}$. To solve this problem, we propose a doubly-optimistic algorithm that employs Lower Confidence Bounds (LCB) for action selection and Upper Confidence Bounds (UCB) for action generation. Empirical evaluation on healthcare question-answering datasets demonstrates that our approach achieves favorable generation-quality tradeoffs compared to baseline strategies. From theoretical perspectives, we prove that our algorithm achieves the optimal regret of $O(T^{\frac{d}{d+2}}d^{\frac{d}{d+2}} + d\sqrt{T\log T})$, providing the first sublinear regret bound for online learning with expanding action spaces.

Yuda Song, J. Andrew Bagnell, Aarti Singh

We consider the hybrid reinforcement learning setting where the agent has access to both offline data and online interactive access. While Reinforcement Learning (RL) research typically assumes offline data contains complete action, reward and transition information, datasets with only state information (also known as observation-only datasets) are more general, abundant and practical. This motivates our study of the hybrid RL with observation-only offline dataset framework. While the task of competing with the best policy "covered" by the offline data can be solved if a reset model of the environment is provided (i.e., one that can be reset to any state), we show evidence of hardness when only given the weaker trace model (i.e., one can only reset to the initial states and must produce full traces through the environment), without further assumption of admissibility of the offline data. Under the admissibility assumptions -- that the offline data could actually be produced by the policy class we consider -- we propose the first algorithm in the trace model setting that provably matches the performance of algorithms that leverage a reset model. We also perform proof-of-concept experiments that suggest the effectiveness of our algorithm in practice.

Yuda Song, Gokul Swamy, Aarti Singh et al.

Learning from human preference data has emerged as the dominant paradigm for fine-tuning large language models (LLMs). The two most common families of techniques -- online reinforcement learning (RL) such as Proximal Policy Optimization (PPO) and offline contrastive methods such as Direct Preference Optimization (DPO) -- were positioned as equivalent in prior work due to the fact that both have to start from the same offline preference dataset. To further expand our theoretical understanding of the similarities and differences between online and offline techniques for preference fine-tuning, we conduct a rigorous analysis through the lens of dataset coverage, a concept that captures how the training data covers the test distribution and is widely used in RL. We prove that a global coverage condition is both necessary and sufficient for offline contrastive methods to converge to the optimal policy, but a weaker partial coverage condition suffices for online RL methods. This separation provides one explanation of why online RL methods can perform better than offline methods, especially when the offline preference data is not diverse enough. Finally, motivated by our preceding theoretical observations, we derive a hybrid preference optimization (HyPO) algorithm that uses offline data for contrastive-based preference optimization and online data for KL regularization. Theoretically and empirically, we demonstrate that HyPO is more performant than its pure offline counterpart DPO, while still preserving its computation and memory efficiency.

Aakash Lahoti, Stefani Karp, Ezra Winston et al.

Vision tasks are characterized by the properties of locality and translation invariance. The superior performance of convolutional neural networks (CNNs) on these tasks is widely attributed to the inductive bias of locality and weight sharing baked into their architecture. Existing attempts to quantify the statistical benefits of these biases in CNNs over locally connected convolutional neural networks (LCNs) and fully connected neural networks (FCNs) fall into one of the following categories: either they disregard the optimizer and only provide uniform convergence upper bounds with no separating lower bounds, or they consider simplistic tasks that do not truly mirror the locality and translation invariance as found in real-world vision tasks. To address these deficiencies, we introduce the Dynamic Signal Distribution (DSD) classification task that models an image as consisting of $k$ patches, each of dimension $d$, and the label is determined by a $d$-sparse signal vector that can freely appear in any one of the $k$ patches. On this task, for any orthogonally equivariant algorithm like gradient descent, we prove that CNNs require $\tilde{O}(k+d)$ samples, whereas LCNs require $Ω(kd)$ samples, establishing the statistical advantages of weight sharing in translation invariant tasks. Furthermore, LCNs need $\tilde{O}(k(k+d))$ samples, compared to $Ω(k^2d)$ samples for FCNs, showcasing the benefits of locality in local tasks. Additionally, we develop information theoretic tools for analyzing randomized algorithms, which may be of interest for statistical research.

Dhruv Malik, Conor Igoe, Yuanzhi Li et al.

In recommender system or crowdsourcing applications of online learning, a human's preferences or abilities are often a function of the algorithm's recent actions. Motivated by this, a significant line of work has formalized settings where an action's loss is a function of the number of times that action was recently played in the prior $m$ timesteps, where $m$ corresponds to a bound on human memory capacity. To more faithfully capture decay of human memory with time, we introduce the Weighted Tallying Bandit (WTB), which generalizes this setting by requiring that an action's loss is a function of a \emph{weighted} summation of the number of times that arm was played in the last $m$ timesteps. This WTB setting is intractable without further assumption. So we study it under Repeated Exposure Optimality (REO), a condition motivated by the literature on human physiology, which requires the existence of an action that when repetitively played will eventually yield smaller loss than any other sequence of actions. We study the minimization of the complete policy regret (CPR), which is the strongest notion of regret, in WTB under REO. Since $m$ is typically unknown, we assume we only have access to an upper bound $M$ on $m$. We show that for problems with $K$ actions and horizon $T$, a simple modification of the successive elimination algorithm has $O \left( \sqrt{KT} + (m+M)K \right)$ CPR. Interestingly, upto an additive (in lieu of mutliplicative) factor in $(m+M)K$, this recovers the classical guarantee for the simpler stochastic multi-armed bandit with traditional regret. We additionally show that in our setting, any algorithm will suffer additive CPR of $Ω\left( mK + M \right)$, demonstrating our result is nearly optimal. Our algorithm is computationally efficient, and we experimentally demonstrate its practicality and superiority over natural baselines.

Ojash Neopane, Aaditya Ramdas, Aarti Singh

We consider a variant of the best arm identification (BAI) problem in multi-armed bandits (MAB) in which there are two sets of arms (source and target), and the objective is to determine the best target arm while only pulling source arms. In this paper, we study the setting when, despite the means being unknown, there is a known additive relationship between the source and target MAB instances. We show how our framework covers a range of previously studied pure exploration problems and additionally captures new problems. We propose and theoretically analyze an LUCB-style algorithm to identify an $ε$-optimal target arm with high probability. Our theoretical analysis highlights aspects of this transfer learning problem that do not arise in the typical BAI setup, and yet recover the LUCB algorithm for single domain BAI as a special case.

Yusha Liu, Yining Wang, Aarti Singh

We consider bandit optimization of a smooth reward function, where the goal is cumulative regret minimization. This problem has been studied for $α$-Hölder continuous (including Lipschitz) functions with $0<α\leq 1$. Our main result is in generalization of the reward function to Hölder space with exponent $α>1$ to bridge the gap between Lipschitz bandits and infinitely-differentiable models such as linear bandits. For Hölder continuous functions, approaches based on random sampling in bins of a discretized domain suffices as optimal. In contrast, we propose a class of two-layer algorithms that deploy misspecified linear/polynomial bandit algorithms in bins. We demonstrate that the proposed algorithm can exploit higher-order smoothness of the function by deriving a regret upper bound of $\tilde{O}(T^\frac{d+α}{d+2α})$ for when $α>1$, which matches existing lower bound. We also study adaptation to unknown function smoothness over a continuous scale of Hölder spaces indexed by $α$, with a bandit model selection approach applied with our proposed two-layer algorithms. We show that it achieves regret rate that matches the existing lower bound for adaptation within the $α\leq 1$ subset.

Ivan Stelmakh, Charvi Rastogi, Nihar B. Shah et al.

Peer review is the backbone of academia and humans constitute a cornerstone of this process, being responsible for reviewing papers and making the final acceptance/rejection decisions. Given that human decision making is known to be susceptible to various cognitive biases, it is important to understand which (if any) biases are present in the peer-review process and design the pipeline such that the impact of these biases is minimized. In this work, we focus on the dynamics of between-reviewers discussions and investigate the presence of herding behaviour therein. In that, we aim to understand whether reviewers and more senior decision makers get disproportionately influenced by the first argument presented in the discussion when (in case of reviewers) they form an independent opinion about the paper before discussing it with others. Specifically, in conjunction with the review process of ICML 2020 -- a large, top tier machine learning conference -- we design and execute a randomized controlled trial with the goal of testing for the conditional causal effect of the discussion initiator's opinion on the outcome of a paper.

Ivan Stelmakh, Nihar B. Shah, Aarti Singh et al.

Conference peer review constitutes a human-computation process whose importance cannot be overstated: not only it identifies the best submissions for acceptance, but, ultimately, it impacts the future of the whole research area by promoting some ideas and restraining others. A surge in the number of submissions received by leading AI conferences has challenged the sustainability of the review process by increasing the burden on the pool of qualified reviewers which is growing at a much slower rate. In this work, we consider the problem of reviewer recruiting with a focus on the scarcity of qualified reviewers in large conferences. Specifically, we design a procedure for (i) recruiting reviewers from the population not typically covered by major conferences and (ii) guiding them through the reviewing pipeline. In conjunction with ICML 2020 -- a large, top-tier machine learning conference -- we recruit a small set of reviewers through our procedure and compare their performance with the general population of ICML reviewers. Our experiment reveals that a combination of the recruiting and guiding mechanisms allows for a principled enhancement of the reviewer pool and results in reviews of superior quality compared to the conventional pool of reviews as evaluated by senior members of the program committee (meta-reviewers).

Ivan Stelmakh, Nihar B. Shah, Aarti Singh et al.

Modern machine learning and computer science conferences are experiencing a surge in the number of submissions that challenges the quality of peer review as the number of competent reviewers is growing at a much slower rate. To curb this trend and reduce the burden on reviewers, several conferences have started encouraging or even requiring authors to declare the previous submission history of their papers. Such initiatives have been met with skepticism among authors, who raise the concern about a potential bias in reviewers' recommendations induced by this information. In this work, we investigate whether reviewers exhibit a bias caused by the knowledge that the submission under review was previously rejected at a similar venue, focusing on a population of novice reviewers who constitute a large fraction of the reviewer pool in leading machine learning and computer science conferences. We design and conduct a randomized controlled trial closely replicating the relevant components of the peer-review pipeline with $133$ reviewers (master's, junior PhD students, and recent graduates of top US universities) writing reviews for $19$ papers. The analysis reveals that reviewers indeed become negatively biased when they receive a signal about paper being a resubmission, giving almost 1 point lower overall score on a 10-point Likert item ($Δ= -0.78, \ 95\% \ \text{CI} = [-1.30, -0.24]$) than reviewers who do not receive such a signal. Looking at specific criteria scores (originality, quality, clarity and significance), we observe that novice reviewers tend to underrate quality the most.

Ivan Stelmakh, Nihar B. Shah, Aarti Singh

We consider the issue of strategic behaviour in various peer-assessment tasks, including peer grading of exams or homeworks and peer review in hiring or promotions. When a peer-assessment task is competitive (e.g., when students are graded on a curve), agents may be incentivized to misreport evaluations in order to improve their own final standing. Our focus is on designing methods for detection of such manipulations. Specifically, we consider a setting in which agents evaluate a subset of their peers and output rankings that are later aggregated to form a final ordering. In this paper, we investigate a statistical framework for this problem and design a principled test for detecting strategic behaviour. We prove that our test has strong false alarm guarantees and evaluate its detection ability in practical settings. For this, we design and execute an experiment that elicits strategic behaviour from subjects and release a dataset of patterns of strategic behaviour that may be of independent interest. We then use the collected data to conduct a series of real and semi-synthetic evaluations that demonstrate a strong detection power of our test.

Nadine Chang, Jayanth Koushik, Aarti Singh et al.

Methods in long-tail learning focus on improving performance for data-poor (rare) classes; however, performance for such classes remains much lower than performance for more data-rich (frequent) classes. Analyzing the predictions of long-tail methods for rare classes reveals that a large number of errors are due to misclassification of rare items as visually similar frequent classes. To address this problem, we introduce AlphaNet, a method that can be applied to existing models, performing post hoc correction on classifiers of rare classes. Starting with a pre-trained model, we find frequent classes that are closest to rare classes in the model's representation space and learn weights to update rare class classifiers with a linear combination of frequent class classifiers. AlphaNet, applied to several models, greatly improves test accuracy for rare classes in multiple long-tailed datasets, with very little change to overall accuracy. Our method also provides a way to control the trade-off between rare class and overall accuracy, making it practical for long-tail classification in the wild.

Charvi Rastogi, Sivaraman Balakrishnan, Nihar B. Shah et al.

A number of applications require two-sample testing on ranked preference data. For instance, in crowdsourcing, there is a long-standing question of whether pairwise comparison data provided by people is distributed similar to ratings-converted-to-comparisons. Other examples include sports data analysis and peer grading. In this paper, we design two-sample tests for pairwise comparison data and ranking data. For our two-sample test for pairwise comparison data, we establish an upper bound on the sample complexity required to correctly distinguish between the distributions of the two sets of samples. Our test requires essentially no assumptions on the distributions. We then prove complementary lower bounds showing that our results are tight (in the minimax sense) up to constant factors. We investigate the role of modeling assumptions by proving lower bounds for a range of pairwise comparison models (WST, MST,SST, parameter-based such as BTL and Thurstone). We also provide testing algorithms and associated sample complexity bounds for the problem of two-sample testing with partial (or total) ranking data.Furthermore, we empirically evaluate our results via extensive simulations as well as two real-world datasets consisting of pairwise comparisons. By applying our two-sample test on real-world pairwise comparison data, we conclude that ratings and rankings provided by people are indeed distributed differently. On the other hand, our test recognizes no significant difference in the relative performance of European football teams across two seasons. Finally, we apply our two-sample test on a real-world partial and total ranking dataset and find a statistically significant difference in Sushi preferences across demographic divisions based on gender, age and region of residence.

Yichong Xu, Ruosong Wang, Lin F. Yang et al.

Preference-based Reinforcement Learning (PbRL) replaces reward values in traditional reinforcement learning by preferences to better elicit human opinion on the target objective, especially when numerical reward values are hard to design or interpret. Despite promising results in applications, the theoretical understanding of PbRL is still in its infancy. In this paper, we present the first finite-time analysis for general PbRL problems. We first show that a unique optimal policy may not exist if preferences over trajectories are deterministic for PbRL. If preferences are stochastic, and the preference probability relates to the hidden reward values, we present algorithms for PbRL, both with and without a simulator, that are able to identify the best policy up to accuracy $\varepsilon$ with high probability. Our method explores the state space by navigating to under-explored states, and solves PbRL using a combination of dueling bandits and policy search. Experiments show the efficacy of our method when it is applied to real-world problems.

Yichong Xu, Aparna Joshi, Aarti Singh et al.

We consider a novel setting of zeroth order non-convex optimization, where in addition to querying the function value at a given point, we can also duel two points and get the point with the larger function value. We refer to this setting as optimization with dueling-choice bandits since both direct queries and duels are available for optimization. We give the COMP-GP-UCB algorithm based on GP-UCB (Srinivas et al., 2009), where instead of directly querying the point with the maximum Upper Confidence Bound (UCB), we perform a constrained optimization and use comparisons to filter out suboptimal points. COMP-GP-UCB comes with theoretical guarantee of $O(\fracΦ{\sqrt{T}})$ on simple regret where $T$ is the number of direct queries and $Φ$ is an improved information gain corresponding to a comparison based constraint set that restricts the search space for the optimum. In contrast, in the direct query only setting, $Φ$ depends on the entire domain. Finally, we present experimental results to show the efficacy of our algorithm.

Yuexin Wu, Yichong Xu, Aarti Singh et al.

Graph Neural Networks (GNNs) for prediction tasks like node classification or edge prediction have received increasing attention in recent machine learning from graphically structured data. However, a large quantity of labeled graphs is difficult to obtain, which significantly limits the true success of GNNs. Although active learning has been widely studied for addressing label-sparse issues with other data types like text, images, etc., how to make it effective over graphs is an open question for research. In this paper, we present an investigation on active learning with GNNs for node classification tasks. Specifically, we propose a new method, which uses node feature propagation followed by K-Medoids clustering of the nodes for instance selection in active learning. With a theoretical bound analysis we justify the design choice of our approach. In our experiments on four benchmark datasets, the proposed method outperforms other representative baseline methods consistently and significantly.

Yichong Xu, Xi Chen, Aarti Singh et al.

The Thresholding Bandit Problem (TBP) aims to find the set of arms with mean rewards greater than a given threshold. We consider a new setting of TBP, where in addition to pulling arms, one can also \emph{duel} two arms and get the arm with a greater mean. In our motivating application from crowdsourcing, dueling two arms can be more cost-effective and time-efficient than direct pulls. We refer to this problem as TBP with Dueling Choices (TBP-DC). This paper provides an algorithm called Rank-Search (RS) for solving TBP-DC by alternating between ranking and binary search. We prove theoretical guarantees for RS, and also give lower bounds to show the optimality of it. Experiments show that RS outperforms previous baseline algorithms that only use pulls or duels.

Yining Wang, Erva Ulu, Aarti Singh et al.

An important task in structural design is to quantify the structural performance of an object under the external forces it may experience during its use. The problem proves to be computationally very challenging as the external forces' contact locations and magnitudes may exhibit significant variations. We present an efficient analysis approach to determine the most critical force contact location in such problems with force location uncertainty. Given an input 3D model and regions on its boundary where arbitrary normal forces may make contact, our algorithm predicts the worst-case force configuration responsible for creating the highest stress within the object. Our approach uses a computationally tractable experimental design method to select number of sample force locations based on geometry only, without inspecting the stress response that requires computationally expensive finite-element analysis. Then, we construct a simple regression model on these samples and corresponding maximum stresses. Combined with a simple ranking based post-processing step, our method provides a practical solution to worst-case structural analysis problem. The results indicate that our approach achieves significant improvements over the existing work and brute force approaches. We demonstrate that further speed- up can be obtained when small amount of an error tolerance in maximum stress is allowed.

Simon S. Du, Xiyu Zhai, Barnabas Poczos et al.

One of the mysteries in the success of neural networks is randomly initialized first order methods like gradient descent can achieve zero training loss even though the objective function is non-convex and non-smooth. This paper demystifies this surprising phenomenon for two-layer fully connected ReLU activated neural networks. For an $m$ hidden node shallow neural network with ReLU activation and $n$ training data, we show as long as $m$ is large enough and no two inputs are parallel, randomly initialized gradient descent converges to a globally optimal solution at a linear convergence rate for the quadratic loss function. Our analysis relies on the following observation: over-parameterization and random initialization jointly restrict every weight vector to be close to its initialization for all iterations, which allows us to exploit a strong convexity-like property to show that gradient descent converges at a global linear rate to the global optimum. We believe these insights are also useful in analyzing deep models and other first order methods.

Ivan Stelmakh, Nihar B. Shah, Aarti Singh

We consider the problem of automated assignment of papers to reviewers in conference peer review, with a focus on fairness and statistical accuracy. Our fairness objective is to maximize the review quality of the most disadvantaged paper, in contrast to the commonly used objective of maximizing the total quality over all papers. We design an assignment algorithm based on an incremental max-flow procedure that we prove is near-optimally fair. Our statistical accuracy objective is to ensure correct recovery of the papers that should be accepted. We provide a sharp minimax analysis of the accuracy of the peer-review process for a popular objective-score model as well as for a novel subjective-score model that we propose in the paper. Our analysis proves that our proposed assignment algorithm also leads to a near-optimal statistical accuracy. Finally, we design a novel experiment that allows for an objective comparison of various assignment algorithms, and overcomes the inherent difficulty posed by the absence of a ground truth in experiments on peer-review. The results of this experiment as well as of other experiments on synthetic and real data corroborate the theoretical guarantees of our algorithm.

Yichong Xu, Sivaraman Balakrishnan, Aarti Singh et al.

In supervised learning, we typically leverage a fully labeled dataset to design methods for function estimation or prediction. In many practical situations, we are able to obtain alternative feedback, possibly at a low cost. A broad goal is to understand the usefulness of, and to design algorithms to exploit, this alternative feedback. In this paper, we consider a semi-supervised regression setting, where we obtain additional ordinal (or comparison) information for the unlabeled samples. We consider ordinal feedback of varying qualities where we have either a perfect ordering of the samples, a noisy ordering of the samples or noisy pairwise comparisons between the samples. We provide a precise quantification of the usefulness of these types of ordinal feedback in both nonparametric and linear regression, showing that in many cases it is possible to accurately estimate an underlying function with a very small labeled set, effectively \emph{escaping the curse of dimensionality}. We also present lower bounds, that establish fundamental limits for the task and show that our algorithms are optimal in a variety of settings. Finally, we present extensive experiments on new datasets that demonstrate the efficacy and practicality of our algorithms and investigate their robustness to various sources of noise and model misspecification.

Simon S. Du, Yining Wang, Sivaraman Balakrishnan et al.

We consider the non-parametric regression problem under Huber's $ε$-contamination model, in which an $ε$ fraction of observations are subject to arbitrary adversarial noise. We first show that a simple local binning median step can effectively remove the adversary noise and this median estimator is minimax optimal up to absolute constants over the Hölder function class with smoothness parameters smaller than or equal to 1. Furthermore, when the underlying function has higher smoothness, we show that using local binning median as pre-preprocessing step to remove the adversarial noise, then we can apply any non-parametric estimator on top of the medians. In particular we show local median binning followed by kernel smoothing and local polynomial regression achieve minimaxity over Hölder and Sobolev classes with arbitrary smoothness parameters. Our main proof technique is a decoupled analysis of adversary noise and stochastic noise, which can be potentially applied to other robust estimation problems. We also provide numerical results to verify the effectiveness of our proposed methods.

Simon S. Du, Yining Wang, Xiyu Zhai et al.

It is widely believed that the practical success of Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) owes to the fact that CNNs and RNNs use a more compact parametric representation than their Fully-Connected Neural Network (FNN) counterparts, and consequently require fewer training examples to accurately estimate their parameters. We initiate the study of rigorously characterizing the sample-complexity of estimating CNNs and RNNs. We show that the sample-complexity to learn CNNs and RNNs scales linearly with their intrinsic dimension and this sample-complexity is much smaller than for their FNN counterparts. For both CNNs and RNNs, we also present lower bounds showing our sample complexities are tight up to logarithmic factors. Our main technical tools for deriving these results are a localized empirical process analysis and a new technical lemma characterizing the convolutional and recurrent structure. We believe that these tools may inspire further developments in understanding CNNs and RNNs.

Yo Joong Choe, Sivaraman Balakrishnan, Aarti Singh et al.

Large bundles of myelinated axons, called white matter, anatomically connect disparate brain regions together and compose the structural core of the human connectome. We recently proposed a method of measuring the local integrity along the length of each white matter fascicle, termed the local connectome. If communication efficiency is fundamentally constrained by the integrity along the entire length of a white matter bundle, then variability in the functional dynamics of brain networks should be associated with variability in the local connectome. We test this prediction using two statistical approaches that are capable of handling the high dimensionality of data. First, by performing statistical inference on distance-based correlations, we show that similarity in the local connectome between individuals is significantly correlated with similarity in their patterns of functional connectivity. Second, by employing variable selection using sparse canonical correlation analysis and cross-validation, we show that segments of the local connectome are predictive of certain patterns of functional brain dynamics. These results are consistent with the hypothesis that structural variability along axon bundles constrains communication between disparate brain regions.

Yining Wang, Sivaraman Balakrishnan, Aarti Singh

We consider the problem of global optimization of an unknown non-convex smooth function with zeroth-order feedback. In this setup, an algorithm is allowed to adaptively query the underlying function at different locations and receives noisy evaluations of function values at the queried points (i.e. the algorithm has access to zeroth-order information). Optimization performance is evaluated by the expected difference of function values at the estimated optimum and the true optimum. In contrast to the classical optimization setup, first-order information like gradients are not directly accessible to the optimization algorithm. We show that the classical minimax framework of analysis, which roughly characterizes the worst-case query complexity of an optimization algorithm in this setting, leads to excessively pessimistic results. We propose a local minimax framework to study the fundamental difficulty of optimizing smooth functions with adaptive function evaluations, which provides a refined picture of the intrinsic difficulty of zeroth-order optimization. We show that for functions with fast level set growth around the global minimum, carefully designed optimization algorithms can identify a near global minimizer with many fewer queries. For the special case of strongly convex and smooth functions, our implied convergence rates match the ones developed for zeroth-order convex optimization problems. At the other end of the spectrum, for worst-case smooth functions no algorithm can converge faster than the minimax rate of estimating the entire unknown function in the $\ell_\infty$-norm. We provide an intuitive and efficient algorithm that attains the derived upper error bounds.

Yifan Wu, Barnabas Poczos, Aarti Singh

A major challenge in understanding the generalization of deep learning is to explain why (stochastic) gradient descent can exploit the network architecture to find solutions that have good generalization performance when using high capacity models. We find simple but realistic examples showing that this phenomenon exists even when learning linear classifiers --- between two linear networks with the same capacity, the one with a convolutional layer can generalize better than the other when the data distribution has some underlying spatial structure. We argue that this difference results from a combination of the convolution architecture, data distribution and gradient descent, all of which are necessary to be included in a meaningful analysis. We provide a general analysis of the generalization performance as a function of data distribution and convolutional filter size, given gradient descent as the optimization algorithm, then interpret the results using concrete examples. Experimental results show that our analysis is able to explain what happens in our introduced examples.

Simon S. Du, Jason D. Lee, Yuandong Tian et al.

We consider the problem of learning a one-hidden-layer neural network with non-overlapping convolutional layer and ReLU activation, i.e., $f(\mathbf{Z}, \mathbf{w}, \mathbf{a}) = \sum_j a_jσ(\mathbf{w}^T\mathbf{Z}_j)$, in which both the convolutional weights $\mathbf{w}$ and the output weights $\mathbf{a}$ are parameters to be learned. When the labels are the outputs from a teacher network of the same architecture with fixed weights $(\mathbf{w}^*, \mathbf{a}^*)$, we prove that with Gaussian input $\mathbf{Z}$, there is a spurious local minimizer. Surprisingly, in the presence of the spurious local minimizer, gradient descent with weight normalization from randomly initialized weights can still be proven to recover the true parameters with constant probability, which can be boosted to probability $1$ with multiple restarts. We also show that with constant probability, the same procedure could also converge to the spurious local minimum, showing that the local minimum plays a non-trivial role in the dynamics of gradient descent. Furthermore, a quantitative analysis shows that the gradient descent dynamics has two phases: it starts off slow, but converges much faster after several iterations.

Zeyuan Allen-Zhu, Yuanzhi Li, Aarti Singh et al.

The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points. Statistical efficiency is measured by optimality criteria, including A(verage), D(eterminant), T(race), E(igen), V(ariance) and G-optimality. Except for the T-optimality, exact optimization is NP-hard. We propose a polynomial-time regret minimization framework to achieve a $(1+\varepsilon)$ approximation with only $O(p/\varepsilon^2)$ design points, for all the optimality criteria above. In contrast, to the best of our knowledge, before our work, no polynomial-time algorithm achieves $(1+\varepsilon)$ approximations for D/E/G-optimality, and the best poly-time algorithm achieving $(1+\varepsilon)$-approximation for A/V-optimality requires $k = Ω(p^2/\varepsilon)$ design points.

Yining Wang, Simon Du, Sivaraman Balakrishnan et al.

We consider the problem of optimizing a high-dimensional convex function using stochastic zeroth-order queries. Under sparsity assumptions on the gradients or function values, we present two algorithms: a successive component/feature selection algorithm and a noisy mirror descent algorithm using Lasso gradient estimates, and show that both algorithms have convergence rates that de- pend only logarithmically on the ambient dimension of the problem. Empirical results confirm our theoretical findings and show that the algorithms we design outperform classical zeroth-order optimization methods in the high-dimensional setting.