Arun Sai Suggala

Dinghuai Zhang, Hongyang Zhang, Aaron Courville et al. · mila

In the context of adversarial robustness, a single model does not usually have enough power to defend against all possible adversarial attacks, and as a result, has sub-optimal robustness. Consequently, an emerging line of work has focused on learning an ensemble of neural networks to defend against adversarial attacks. In this work, we take a principled approach towards building robust ensembles. We view this problem from the perspective of margin-boosting and develop an algorithm for learning an ensemble with maximum margin. Through extensive empirical evaluation on benchmark datasets, we show that our algorithm not only outperforms existing ensembling techniques, but also large models trained in an end-to-end fashion. An important byproduct of our work is a margin-maximizing cross-entropy (MCE) loss, which is a better alternative to the standard cross-entropy (CE) loss. Empirically, we show that replacing the CE loss in state-of-the-art adversarial training techniques with our MCE loss leads to significant performance improvement.

Xiyang Liu, Prateek Jain, Weihao Kong et al.

We study the canonical statistical estimation problem of linear regression from $n$ i.i.d.~examples under $(\varepsilon,δ)$-differential privacy when some response variables are adversarially corrupted. We propose a variant of the popular differentially private stochastic gradient descent (DP-SGD) algorithm with two innovations: a full-batch gradient descent to improve sample complexity and a novel adaptive clipping to guarantee robustness. When there is no adversarial corruption, this algorithm improves upon the existing state-of-the-art approach and achieves a near optimal sample complexity. Under label-corruption, this is the first efficient linear regression algorithm to guarantee both $(\varepsilon,δ)$-DP and robustness. Synthetic experiments confirm the superiority of our approach.

Anja Surina, Arun Suggala, George Tsoukalas et al.

We analyze the last-iterate convergence of the Anchored Gradient Descent Ascent algorithm for smooth convex-concave min-max problems. While previous work established a last-iterate rate of $\mathcal{O}(1/t^{2-2p})$ for the squared gradient norm, where $p \in (1/2, 1)$, it remained an open problem whether the improved exact $\mathcal{O}(1/t)$ rate is achievable. In this work, we resolve this question in the affirmative. This result was discovered autonomously by an AI system capable of writing formal proofs in Lean. The Lean proof can be accessed at https://github.com/google-deepmind/formal-conjectures/pull/3675/commits/a13226b49fd3b897f4c409194f3bcbeb96a08515

Shubhada Agrawal, Sandeep Juneja, Karthikeyan Shanmugam et al.

Learning paradigms based purely on offline data as well as those based solely on sequential online learning have been well-studied in the literature. In this paper, we consider combining offline data with online learning, an area less studied but of obvious practical importance. We consider the stochastic $K$-armed bandit problem, where our goal is to identify the arm with the highest mean in the presence of relevant offline data, with confidence $1-δ$. We conduct a lower bound analysis on policies that provide such $1-δ$ probabilistic correctness guarantees. We develop algorithms that match the lower bound on sample complexity when $δ$ is small. Our algorithms are computationally efficient with an average per-sample acquisition cost of $\tilde{O}(K)$, and rely on a careful characterization of the optimality conditions of the lower bound problem.

Soumyabrata Pal, Arun Sai Suggala, Karthikeyan Shanmugam et al.

We consider the problem of latent bandits with cluster structure where there are multiple users, each with an associated multi-armed bandit problem. These users are grouped into \emph{latent} clusters such that the mean reward vectors of users within the same cluster are identical. At each round, a user, selected uniformly at random, pulls an arm and observes a corresponding noisy reward. The goal of the users is to maximize their cumulative rewards. This problem is central to practical recommendation systems and has received wide attention of late \cite{gentile2014online, maillard2014latent}. Now, if each user acts independently, then they would have to explore each arm independently and a regret of $Ω(\sqrt{\mathsf{MNT}})$ is unavoidable, where $\mathsf{M}, \mathsf{N}$ are the number of arms and users, respectively. Instead, we propose LATTICE (Latent bAndiTs via maTrIx ComplEtion) which allows exploitation of the latent cluster structure to provide the minimax optimal regret of $\widetilde{O}(\sqrt{(\mathsf{M}+\mathsf{N})\mathsf{T}})$, when the number of clusters is $\widetilde{O}(1)$. This is the first algorithm to guarantee such strong regret bound. LATTICE is based on a careful exploitation of arm information within a cluster while simultaneously clustering users. Furthermore, it is computationally efficient and requires only $O(\log{\mathsf{T}})$ calls to an offline matrix completion oracle across all $\mathsf{T}$ rounds.

Ramnath Kumar, Kushal Majmundar, Dheeraj Nagaraj et al.

We present Re-weighted Gradient Descent (RGD), a novel optimization technique that improves the performance of deep neural networks through dynamic sample re-weighting. Leveraging insights from distributionally robust optimization (DRO) with Kullback-Leibler divergence, our method dynamically assigns importance weights to training data during each optimization step. RGD is simple to implement, computationally efficient, and compatible with widely used optimizers such as SGD and Adam. We demonstrate the effectiveness of RGD on various learning tasks, including supervised learning, meta-learning, and out-of-domain generalization. Notably, RGD achieves state-of-the-art results on diverse benchmarks, with improvements of +0.7% on DomainBed, +1.44% on tabular classification, \textcolor{blue}+1.94% on GLUE with BERT, and +1.01% on ImageNet-1K with ViT.

Soumyabrata Pal, Arun Sai Suggala, Karthikeyan Shanmugam et al.

We consider the problem of \emph{blocked} collaborative bandits where there are multiple users, each with an associated multi-armed bandit problem. These users are grouped into \emph{latent} clusters such that the mean reward vectors of users within the same cluster are identical. Our goal is to design algorithms that maximize the cumulative reward accrued by all the users over time, under the \emph{constraint} that no arm of a user is pulled more than $\mathsf{B}$ times. This problem has been originally considered by \cite{Bresler:2014}, and designing regret-optimal algorithms for it has since remained an open problem. In this work, we propose an algorithm called \texttt{B-LATTICE} (Blocked Latent bAndiTs via maTrIx ComplEtion) that collaborates across users, while simultaneously satisfying the budget constraints, to maximize their cumulative rewards. Theoretically, under certain reasonable assumptions on the latent structure, with $\mathsf{M}$ users, $\mathsf{N}$ arms, $\mathsf{T}$ rounds per user, and $\mathsf{C}=O(1)$ latent clusters, \texttt{B-LATTICE} achieves a per-user regret of $\widetilde{O}(\sqrt{\mathsf{T}(1 + \mathsf{N}\mathsf{M}^{-1})}$ under a budget constraint of $\mathsf{B}=Θ(\log \mathsf{T})$. These are the first sub-linear regret bounds for this problem, and match the minimax regret bounds when $\mathsf{B}=\mathsf{T}$. Empirically, we demonstrate that our algorithm has superior performance over baselines even when $\mathsf{B}=1$. \texttt{B-LATTICE} runs in phases where in each phase it clusters users into groups and collaborates across users within a group to quickly learn their reward models.

Yash Gupta, Runtian Zhai, Arun Suggala et al.

Several recent works have studied the societal effects of AI; these include issues such as fairness, robustness, and safety. In many of these objectives, a learner seeks to minimize its worst-case loss over a set of predefined distributions (known as uncertainty sets), with usual examples being perturbed versions of the empirical distribution. In other words, aforementioned problems can be written as min-max problems over these uncertainty sets. In this work, we provide a general framework for studying these problems, which we refer to as Responsible AI (RAI) games. We provide two classes of algorithms for solving these games: (a) game-play based algorithms, and (b) greedy stagewise estimation algorithms. The former class is motivated by online learning and game theory, whereas the latter class is motivated by the classical statistical literature on boosting, and regression. We empirically demonstrate the applicability and competitive performance of our techniques for solving several RAI problems, particularly around subpopulation shift.

Anshul Nasery, Hardik Shah, Arun Sai Suggala et al.

Neural network (NN) compression via techniques such as pruning, quantization requires setting compression hyperparameters (e.g., number of channels to be pruned, bitwidths for quantization) for each layer either manually or via neural architecture search (NAS) which can be computationally expensive. We address this problem by providing an end-to-end technique that optimizes for model's Floating Point Operations (FLOPs) or for on-device latency via a novel $\frac{\ell_1}{\ell_2}$ latency surrogate. Our algorithm is versatile and can be used with many popular compression methods including pruning, low-rank factorization, and quantization. Crucially, it is fast and runs in almost the same amount of time as single model training; which is a significant training speed-up over standard NAS methods. For BERT compression on GLUE fine-tuning tasks, we achieve $50\%$ reduction in FLOPs with only $1\%$ drop in performance. For compressing MobileNetV3 on ImageNet-1K, we achieve $15\%$ reduction in FLOPs, and $11\%$ reduction in on-device latency without drop in accuracy, while still requiring $3\times$ less training compute than SOTA compression techniques. Finally, for transfer learning on smaller datasets, our technique identifies $1.2\times$-$1.4\times$ cheaper architectures than standard MobileNetV3, EfficientNet suite of architectures at almost the same training cost and accuracy.

Wesley Tansey, Oscar Hernan Madrid Padilla, Arun Sai Suggala et al.

We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter exponential family and mixed graphical models, thereby greatly broadening the class of exponential families available (e.g., allowing multinomial and Dirichlet distributions). Specifically, VS-MRFs are the joint graphical model distributions where the node-conditional distributions belong to generic exponential families with general vector space domains. We also present a sparsistent $M$-estimator for learning our class of MRFs that recovers the correct set of edges with high probability. We validate our approach via a set of synthetic data experiments as well as a real-world case study of over four million foods from the popular diet tracking app MyFitnessPal. Our results demonstrate that our algorithm performs well empirically and that VS-MRFs are capable of capturing and highlighting interesting structure in complex, real-world data. All code for our algorithm is open source and publicly available.

Dravyansh Sharma, Arun Sai Suggala

Classic algorithms for stochastic bandits typically use hyperparameters that govern their critical properties such as the trade-off between exploration and exploitation. Tuning these hyperparameters is a problem of great practical significance. However, this is a challenging problem and in certain cases is information theoretically impossible. To address this challenge, we consider a practically relevant transfer learning setting where one has access to offline data collected from several bandit problems (tasks) coming from an unknown distribution over the tasks. Our aim is to use this offline data to set the hyperparameters for a new task drawn from the unknown distribution. We provide bounds on the inter-task (number of tasks) and intra-task (number of arm pulls for each task) sample complexity for learning near-optimal hyperparameters on unseen tasks drawn from the distribution. Our results apply to several classic algorithms, including tuning the exploration parameters in UCB and LinUCB and the noise parameter in GP-UCB. Our experiments indicate the significance and effectiveness of the transfer of hyperparameters from offline problems in online learning with stochastic bandit feedback.

Sravanti Addepalli, Yerram Varun, Arun Suggala et al.

Large Language Models (LLMs) are known to be susceptible to crafted adversarial attacks or jailbreaks that lead to the generation of objectionable content despite being aligned to human preferences using safety fine-tuning methods. While the large dimensionality of input token space makes it inevitable to find adversarial prompts that can jailbreak these models, we aim to evaluate whether safety fine-tuned LLMs are safe against natural prompts which are semantically related to toxic seed prompts that elicit safe responses after alignment. We surprisingly find that popular aligned LLMs such as GPT-4 can be compromised using naive prompts that are NOT even crafted with an objective of jailbreaking the model. Furthermore, we empirically show that given a seed prompt that elicits a toxic response from an unaligned model, one can systematically generate several semantically related natural prompts that can jailbreak aligned LLMs. Towards this, we propose a method of Response Guided Question Augmentation (ReG-QA) to evaluate the generalization of safety aligned LLMs to natural prompts, that first generates several toxic answers given a seed question using an unaligned LLM (Q to A), and further leverages an LLM to generate questions that are likely to produce these answers (A to Q). We interestingly find that safety fine-tuned LLMs such as GPT-4o are vulnerable to producing natural jailbreak questions from unsafe content (without denial) and can thus be used for the latter (A to Q) step. We obtain attack success rates that are comparable to/ better than leading adversarial attack methods on the JailbreakBench leaderboard, while being significantly more stable against defenses such as Smooth-LLM and Synonym Substitution, which are effective against existing all attacks on the leaderboard.

Nishant Jain, Arun S. Suggala, Pradeep Shenoy

Learned reweighting (LRW) approaches to supervised learning use an optimization criterion to assign weights for training instances, in order to maximize performance on a representative validation dataset. We pose and formalize the problem of optimized selection of the validation set used in LRW training, to improve classifier generalization. In particular, we show that using hard-to-classify instances in the validation set has both a theoretical connection to, and strong empirical evidence of generalization. We provide an efficient algorithm for training this meta-optimized model, as well as a simple train-twice heuristic for careful comparative study. We demonstrate that LRW with easy validation data performs consistently worse than LRW with hard validation data, establishing the validity of our meta-optimization problem. Our proposed algorithm outperforms a wide range of baselines on a range of datasets and domain shift challenges (Imagenet-1K, CIFAR-100, Clothing-1M, CAMELYON, WILDS, etc.), with ~1% gains using VIT-B on Imagenet. We also show that using naturally hard examples for validation (Imagenet-R / Imagenet-A) in LRW training for Imagenet improves performance on both clean and naturally hard test instances by 1-2%. Secondary analyses show that using hard validation data in an LRW framework improves margins on test data, hinting at the mechanism underlying our empirical gains. We believe this work opens up new research directions for the meta-optimization of meta-learning in a supervised learning context.

Sushant Vijayan, Zhe Feng, Swati Padmanabhan et al.

We consider the problem of bidding in online advertising, where an advertiser aims to maximize value while adhering to budget and Return-on-Spend (RoS) constraints. Unlike prior work that assumes knowledge of the value generated by winning each impression ({e.g.,} conversions), we address the more realistic setting where the advertiser must simultaneously learn the optimal bidding strategy and the value of each impression opportunity. This introduces a challenging exploration-exploitation dilemma: the advertiser must balance exploring different bids to estimate impression values with exploiting current knowledge to bid effectively. To address this, we propose a novel Upper Confidence Bound (UCB)-style algorithm that carefully manages this trade-off. Via a rigorous theoretical analysis, we prove that our algorithm achieves $\widetilde{O}(\sqrt{T\log(|\mathcal{B}|T)})$ regret and constraint violation, where $T$ is the number of bidding rounds and $\mathcal{B}$ is the domain of possible bids. This establishes the first optimal regret and constraint violation bounds for bidding in the online setting with unknown impression values. Moreover, our algorithm is computationally efficient and simple to implement. We validate our theoretical findings through experiments on synthetic data, demonstrating that our algorithm exhibits strong empirical performance compared to existing approaches.

Aniket Das, Dheeraj Nagaraj, Soumyabrata Pal et al.

We consider the problem of high-dimensional heavy-tailed statistical estimation in the streaming setting, which is much harder than the traditional batch setting due to memory constraints. We cast this problem as stochastic convex optimization with heavy tailed stochastic gradients, and prove that the widely used Clipped-SGD algorithm attains near-optimal sub-Gaussian statistical rates whenever the second moment of the stochastic gradient noise is finite. More precisely, with $T$ samples, we show that Clipped-SGD, for smooth and strongly convex objectives, achieves an error of $\sqrt{\frac{\mathsf{Tr}(Σ)+\sqrt{\mathsf{Tr}(Σ)\|Σ\|_2}\log(\frac{\log(T)}δ)}{T}}$ with probability $1-δ$, where $Σ$ is the covariance of the clipped gradient. Note that the fluctuations (depending on $\frac{1}δ$) are of lower order than the term $\mathsf{Tr}(Σ)$. This improves upon the current best rate of $\sqrt{\frac{\mathsf{Tr}(Σ)\log(\frac{1}δ)}{T}}$ for Clipped-SGD, known only for smooth and strongly convex objectives. Our results also extend to smooth convex and lipschitz convex objectives. Key to our result is a novel iterative refinement strategy for martingale concentration, improving upon the PAC-Bayes approach of Catoni and Giulini.

Arun Suggala, Y. Jennifer Sun, Praneeth Netrapalli et al. · princeton

Bandit convex optimization (BCO) is a general framework for online decision making under uncertainty. While tight regret bounds for general convex losses have been established, existing algorithms achieving these bounds have prohibitive computational costs for high dimensional data. In this paper, we propose a simple and practical BCO algorithm inspired by the online Newton step algorithm. We show that our algorithm achieves optimal (in terms of horizon) regret bounds for a large class of convex functions that we call $κ$-convex. This class contains a wide range of practically relevant loss functions including linear, quadratic, and generalized linear models. In addition to optimal regret, this method is the most efficient known algorithm for several well-studied applications including bandit logistic regression. Furthermore, we investigate the adaptation of our second-order bandit algorithm to online convex optimization with memory. We show that for loss functions with a certain affine structure, the extended algorithm attains optimal regret. This leads to an algorithm with optimal regret for bandit LQR/LQG problems under a fully adversarial noise model, thereby resolving an open question posed in \citep{gradu2020non} and \citep{sun2023optimal}. Finally, we show that the more general problem of BCO with (non-affine) memory is harder. We derive a $\tildeΩ(T^{2/3})$ regret lower bound, even under the assumption of smooth and quadratic losses.

Yerram Varun, Rahul Madhavan, Sravanti Addepalli et al.

Large Language Models (LLMs) are typically trained to predict in the forward direction of time. However, recent works have shown that prompting these models to look back and critique their own generations can produce useful feedback. Motivated by this, we explore the question of whether LLMs can be empowered to think (predict and score) backwards to provide unsupervised feedback that complements forward LLMs. Towards this, we introduce Time Reversed Language Models (TRLMs), which can score and generate queries when conditioned on responses, effectively functioning in the reverse direction of time. Further, to effectively infer in the response to query direction, we pre-train and fine-tune a language model (TRLM-Ba) in the reverse token order from scratch. We show empirically (and theoretically in a stylized setting) that time-reversed models can indeed complement forward model predictions when used to score the query given response for re-ranking multiple forward generations. We obtain up to 5\% improvement on the widely used AlpacaEval Leaderboard over the competent baseline of best-of-N re-ranking using self log-perplexity scores. We further show that TRLM scoring outperforms conventional forward scoring of response given query, resulting in significant gains in applications such as citation generation and passage retrieval. We next leverage the generative ability of TRLM to augment or provide unsupervised feedback to input safety filters of LLMs, demonstrating a drastic reduction in false negative rate with negligible impact on false positive rates against several attacks published on the popular JailbreakBench leaderboard.

Sushant Vijayan, Arun Suggala, Karthikeyan Shanmugam et al.

We consider the problem of online regret minimization in linear bandits with access to prior observations (offline data) from the underlying bandit model. There are numerous applications where extensive offline data is often available, such as in recommendation systems, online advertising. Consequently, this problem has been studied intensively in recent literature. Our algorithm, Offline-Online Phased Elimination (OOPE), effectively incorporates the offline data to substantially reduce the online regret compared to prior work. To leverage offline information prudently, OOPE uses an extended D-optimal design within each exploration phase. OOPE achieves an online regret is $\tilde{O}(\sqrt{\deff T \log \left(|\mathcal{A}|T\right)}+d^2)$. $\deff \leq d)$ is the effective problem dimension which measures the number of poorly explored directions in offline data and depends on the eigen-spectrum $(λ_k)_{k \in [d]}$ of the Gram matrix of the offline data. The eigen-spectrum $(λ_k)_{k \in [d]}$ is a quantitative measure of the \emph{quality} of offline data. If the offline data is poorly explored ($\deff \approx d$), we recover the established regret bounds for purely online setting while, when offline data is abundant ($\Toff >> T$) and well-explored ($\deff = o(1) $), the online regret reduces substantially. Additionally, we provide the first known minimax regret lower bounds in this setting that depend explicitly on the quality of the offline data. These lower bounds establish the optimality of our algorithm in regimes where offline data is either well-explored or poorly explored. Finally, by using a Frank-Wolfe approximation to the extended optimal design we further improve the $O(d^{2})$ term to $O\left(\frac{d^{2}}{\deff} \min \{ \deff,1\} \right)$, which can be substantial in high dimensions with moderate quality of offline data $\deff = Ω(1)$.

Arpan Dasgupta, Mizhaan Maniyar, Awadhesh Srivastava et al.

Mobile health (mHealth) programs utilize automated voice messages to deliver health information, particularly targeting underserved communities, demonstrating the effectiveness of using mobile technology to disseminate crucial health information to these populations, improving health outcomes through increased awareness and behavioral change. India's Kilkari program delivers vital maternal health information via weekly voice calls to millions of mothers. However, the current random call scheduling often results in missed calls and reduced message delivery. This study presents a field trial of a collaborative bandit algorithm designed to optimize call timing by learning individual mothers' preferred call times. We deployed the algorithm with around $6500$ Kilkari participants as a pilot study, comparing its performance to the baseline random calling approach. Our results demonstrate a statistically significant improvement in call pick-up rates with the bandit algorithm, indicating its potential to enhance message delivery and impact millions of mothers across India. This research highlights the efficacy of personalized scheduling in mobile health interventions and underscores the potential of machine learning to improve maternal health outreach at scale.

Arpan Dasgupta, Gagan Jain, Arun Suggala et al.

Mobile health (mHealth) programs face a critical challenge in optimizing the timing of automated health information calls to beneficiaries. This challenge has been formulated as a collaborative multi-armed bandit problem, requiring online learning of a low-rank reward matrix. Existing solutions often rely on heuristic combinations of offline matrix completion and exploration strategies. In this work, we propose a principled Bayesian approach using Thompson Sampling for this collaborative bandit problem. Our method leverages prior information through efficient Gibbs sampling for posterior inference over the low-rank matrix factors, enabling faster convergence. We demonstrate significant improvements over state-of-the-art baselines on a real-world dataset from the world's largest maternal mHealth program. Our approach achieves a $16\%$ reduction in the number of calls compared to existing methods and a $47$\% reduction compared to the deployed random policy. This efficiency gain translates to a potential increase in program capacity by $0.5-1.4$ million beneficiaries, granting them access to vital ante-natal and post-natal care information. Furthermore, we observe a $7\%$ and $29\%$ improvement in beneficiary retention (an extremely hard metric to impact) compared to state-of-the-art and deployed baselines, respectively. Synthetic simulations further demonstrate the superiority of our approach, particularly in low-data regimes and in effectively utilizing prior information. We also provide a theoretical analysis of our algorithm in a special setting using Eluder dimension.

Pranav Ajit Nair, Arun Sai Suggala

Large language models (LLMs) have recently demonstrated remarkable performance across diverse language tasks. But their deployment is often constrained by their substantial computational and storage requirements. Quantization has emerged as a key technique for addressing this challenge, enabling the compression of large models with minimal impact on performance. The recent GPTQ algorithm, a post-training quantization (PTQ) method, has proven highly effective for compressing LLMs, sparking a wave of research that leverages GPTQ as a core component. Recognizing the pivotal role of GPTQ in the PTQ landscape, we introduce CDQuant, a simple and scalable alternative to GPTQ with improved performance. CDQuant uses greedy coordinate descent to minimize the layer-wise reconstruction loss to achieve high-quality quantized weights. Our algorithm is easy to implement and scales efficiently to models with hundreds of billions of parameters. We perform extensive evaluation on Gemma, and PaLM2 model families, and demonstrate that CDQuant consistently outperforms GPTQ in 2-4 bit weight quantization. Moreover, CDQuant improves the performance of state-of-the-art PTQ techniques such as QuIP and FrameQuant when used as a replacement for their GPTQ component, resulting in further gains in quality.

Sanket Shah, Arun Suggala, Milind Tambe et al.

The declining participation of beneficiaries over time is a key concern in public health programs. A popular strategy for improving retention is to have health workers `intervene' on beneficiaries at risk of dropping out. However, the availability and time of these health workers are limited resources. As a result, there has been a line of research on optimizing these limited intervention resources using Restless Multi-Armed Bandits (RMABs). The key technical barrier to using this framework in practice lies in the need to estimate the beneficiaries' RMAB parameters from historical data. Recent research has shown that Decision-Focused Learning (DFL), which focuses on maximizing the beneficiaries' adherence rather than predictive accuracy, improves the performance of intervention targeting using RMABs. Unfortunately, these gains come at a high computational cost because of the need to solve and evaluate the RMAB in each DFL training step. In this paper, we provide a principled way to exploit the structure of RMABs to speed up intervention planning by cleverly decoupling the planning for different beneficiaries. We use real-world data from an Indian NGO, ARMMAN, to show that our approach is up to two orders of magnitude faster than the state-of-the-art approach while also yielding superior model performance. This would enable the NGO to scale up deployments using DFL to potentially millions of mothers, ultimately advancing progress toward UNSDG 3.1.

Runtian Zhai, Chen Dan, Arun Sai Suggala et al.

Many modern machine learning tasks require models with high tail performance, i.e. high performance over the worst-off samples in the dataset. This problem has been widely studied in fields such as algorithmic fairness, class imbalance, and risk-sensitive decision making. A popular approach to maximize the model's tail performance is to minimize the CVaR (Conditional Value at Risk) loss, which computes the average risk over the tails of the loss. However, for classification tasks where models are evaluated by the zero-one loss, we show that if the classifiers are deterministic, then the minimizer of the average zero-one loss also minimizes the CVaR zero-one loss, suggesting that CVaR loss minimization is not helpful without additional assumptions. We circumvent this negative result by minimizing the CVaR loss over randomized classifiers, for which the minimizers of the average zero-one loss and the CVaR zero-one loss are no longer the same, so minimizing the latter can lead to better tail performance. To learn such randomized classifiers, we propose the Boosted CVaR Classification framework which is motivated by a direct relationship between CVaR and a classical boosting algorithm called LPBoost. Based on this framework, we design an algorithm called $α$-AdaLPBoost. We empirically evaluate our proposed algorithm on four benchmark datasets and show that it achieves higher tail performance than deterministic model training methods.

Kartik Gupta, Arun Sai Suggala, Adarsh Prasad et al.

We consider the problem of designing minimax estimators for estimating the parameters of a probability distribution. Unlike classical approaches such as the MLE and minimum distance estimators, we consider an algorithmic approach for constructing such estimators. We view the problem of designing minimax estimators as finding a mixed strategy Nash equilibrium of a zero-sum game. By leveraging recent results in online learning with non-convex losses, we provide a general algorithm for finding a mixed-strategy Nash equilibrium of general non-convex non-concave zero-sum games. Our algorithm requires access to two subroutines: (a) one which outputs a Bayes estimator corresponding to a given prior probability distribution, and (b) one which computes the worst-case risk of any given estimator. Given access to these two subroutines, we show that our algorithm outputs both a minimax estimator and a least favorable prior. To demonstrate the power of this approach, we use it to construct provably minimax estimators for classical problems such as estimation in the finite Gaussian sequence model, and linear regression.

Arun Sai Suggala, Praneeth Netrapalli

We consider the problem of online learning and its application to solving minimax games. For the online learning problem, Follow the Perturbed Leader (FTPL) is a widely studied algorithm which enjoys the optimal $O(T^{1/2})$ worst-case regret guarantee for both convex and nonconvex losses. In this work, we show that when the sequence of loss functions is predictable, a simple modification of FTPL which incorporates optimism can achieve better regret guarantees, while retaining the optimal worst-case regret guarantee for unpredictable sequences. A key challenge in obtaining these tighter regret bounds is the stochasticity and optimism in the algorithm, which requires different analysis techniques than those commonly used in the analysis of FTPL. The key ingredient we utilize in our analysis is the dual view of perturbation as regularization. While our algorithm has several applications, we consider the specific application of minimax games. For solving smooth convex-concave games, our algorithm only requires access to a linear optimization oracle. For Lipschitz and smooth nonconvex-nonconcave games, our algorithm requires access to an optimization oracle which computes the perturbed best response. In both these settings, our algorithm solves the game up to an accuracy of $O(T^{-1/2})$ using $T$ calls to the optimization oracle. An important feature of our algorithm is that it is highly parallelizable and requires only $O(T^{1/2})$ iterations, with each iteration making $O(T^{1/2})$ parallel calls to the optimization oracle.

Arun Sai Suggala, Kush Bhatia, Pradeep Ravikumar et al.

We study the problem of robust linear regression with response variable corruptions. We consider the oblivious adversary model, where the adversary corrupts a fraction of the responses in complete ignorance of the data. We provide a nearly linear time estimator which consistently estimates the true regression vector, even with $1-o(1)$ fraction of corruptions. Existing results in this setting either don't guarantee consistent estimates or can only handle a small fraction of corruptions. We also extend our estimator to robust sparse linear regression and show that similar guarantees hold in this setting. Finally, we apply our estimator to the problem of linear regression with heavy-tailed noise and show that our estimator consistently estimates the regression vector even when the noise has unbounded variance (e.g., Cauchy distribution), for which most existing results don't even apply. Our estimator is based on a novel variant of outlier removal via hard thresholding in which the threshold is chosen adaptively and crucially relies on randomness to escape bad fixed points of the non-convex hard thresholding operation.

Arun Sai Suggala, Praneeth Netrapalli

We study the problem of online learning with non-convex losses, where the learner has access to an offline optimization oracle. We show that the classical Follow the Perturbed Leader (FTPL) algorithm achieves optimal regret rate of $O(T^{-1/2})$ in this setting. This improves upon the previous best-known regret rate of $O(T^{-1/3})$ for FTPL. We further show that an optimistic variant of FTPL achieves better regret bounds when the sequence of losses encountered by the learner is `predictable'.

Chih-Kuan Yeh, Cheng-Yu Hsieh, Arun Sai Suggala et al.

We consider objective evaluation measures of saliency explanations for complex black-box machine learning models. We propose simple robust variants of two notions that have been considered in recent literature: (in)fidelity, and sensitivity. We analyze optimal explanations with respect to both these measures, and while the optimal explanation for sensitivity is a vacuous constant explanation, the optimal explanation for infidelity is a novel combination of two popular explanation methods. By varying the perturbation distribution that defines infidelity, we obtain novel explanations by optimizing infidelity, which we show to out-perform existing explanations in both quantitative and qualitative measurements. Another salient question given these measures is how to modify any given explanation to have better values with respect to these measures. We propose a simple modification based on lowering sensitivity, and moreover show that when done appropriately, we could simultaneously improve both sensitivity as well as fidelity.

Arun Sai Suggala, Adarsh Prasad, Vaishnavh Nagarajan et al.

Recent works on adversarial perturbations show that there is an inherent trade-off between standard test accuracy and adversarial accuracy. Specifically, they show that no classifier can simultaneously be robust to adversarial perturbations and achieve high standard test accuracy. However, this is contrary to the standard notion that on tasks such as image classification, humans are robust classifiers with low error rate. In this work, we show that the main reason behind this confusion is the inexact definition of adversarial perturbation that is used in the literature. To fix this issue, we propose a slight, yet important modification to the existing definition of adversarial perturbation. Based on the modified definition, we show that there is no trade-off between adversarial and standard accuracies; there exist classifiers that are robust and achieve high standard accuracy. We further study several properties of this new definition of adversarial risk and its relation to the existing definition.

Adarsh Prasad, Arun Sai Suggala, Sivaraman Balakrishnan et al.

We provide a new computationally-efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models: in the classical Huber epsilon-contamination model and in heavy-tailed settings. Our workhorse is a novel robust variant of gradient descent, and we provide conditions under which our gradient descent variant provides accurate estimators in a general convex risk minimization problem. We provide specific consequences of our theory for linear regression, logistic regression and for estimation of the canonical parameters in an exponential family. These results provide some of the first computationally tractable and provably robust estimators for these canonical statistical models. Finally, we study the empirical performance of our proposed methods on synthetic and real datasets, and find that our methods convincingly outperform a variety of baselines.