Eric Zhao

Nika Haghtalab, Michael I. Jordan, Eric Zhao

Social and real-world considerations such as robustness, fairness, social welfare and multi-agent tradeoffs have given rise to multi-distribution learning paradigms, such as collaborative learning, group distributionally robust optimization, and fair federated learning. In each of these settings, a learner seeks to uniformly minimize its expected loss over $n$ predefined data distributions, while using as few samples as possible. In this paper, we establish the optimal sample complexity of these learning paradigms and give algorithms that meet this sample complexity. Importantly, our sample complexity bounds for multi-distribution learning exceed that of learning a single distribution by only an additive factor of $n \log(n) / ε^2$. This improves upon the best known sample complexity bounds for fair federated learning by Mohri et al. and collaborative learning by Nguyen and Zakynthinou by multiplicative factors of $n$ and $\log(n)/ε^3$, respectively. We also provide the first sample complexity bounds for the group DRO objective of Sagawa et al. To guarantee these optimal sample complexity bounds, our algorithms learn to sample from data distributions on demand. Our algorithm design and analysis are enabled by our extensions of online learning techniques for solving stochastic zero-sum games. In particular, we contribute stochastic variants of no-regret dynamics that can trade off between players' differing sampling costs.

Nika Haghtalab, Michael I. Jordan, Eric Zhao

We provide a unifying framework for the design and analysis of multicalibrated predictors. By placing the multicalibration problem in the general setting of multi-objective learning -- where learning guarantees must hold simultaneously over a set of distributions and loss functions -- we exploit connections to game dynamics to achieve state-of-the-art guarantees for a diverse set of multicalibration learning problems. In addition to shedding light on existing multicalibration guarantees and greatly simplifying their analysis, our approach also yields improved guarantees, such as obtaining stronger multicalibration conditions that scale with the square-root of group size and improving the complexity of $k$-class multicalibration by an exponential factor of $k$. Beyond multicalibration, we use these game dynamics to address emerging considerations in the study of group fairness and multi-distribution learning.

Nika Haghtalab, Mingda Qiao, Kunhe Yang et al.

We initiate the study of the truthfulness of calibration measures in sequential prediction. A calibration measure is said to be truthful if the forecaster (approximately) minimizes the expected penalty by predicting the conditional expectation of the next outcome, given the prior distribution of outcomes. Truthfulness is an important property of calibration measures, ensuring that the forecaster is not incentivized to exploit the system with deliberate poor forecasts. This makes it an essential desideratum for calibration measures, alongside typical requirements, such as soundness and completeness. We conduct a taxonomy of existing calibration measures and their truthfulness. Perhaps surprisingly, we find that all of them are far from being truthful. That is, under existing calibration measures, there are simple distributions on which a polylogarithmic (or even zero) penalty is achievable, while truthful prediction leads to a polynomial penalty. Our main contribution is the introduction of a new calibration measure termed the Subsampled Smooth Calibration Error (SSCE) under which truthful prediction is optimal up to a constant multiplicative factor.

Sivaraman Balakrishnan, Nika Haghtalab, Daniel Hsu et al.

Supervised learning is classically formulated as training a model to minimize a fixed loss function over a fixed distribution, or task. However, an emerging paradigm instead views model training as extracting enough information from data so that the model can be used to minimize many losses on many downstream tasks. We formalize a mathematical framework for this paradigm, which we call panprediction, and study its statistical complexity. Formally, panprediction generalizes omniprediction and sits upstream from multi-group learning, which respectively focus on predictions that generalize to many downstream losses or many downstream tasks, but not both. Concretely, we design algorithms that learn deterministic and randomized panpredictors with $\tilde{O}(1/\varepsilon^3)$ and $\tilde{O}(1/\varepsilon^2)$ samples, respectively. Our results demonstrate that under mild assumptions, simultaneously minimizing infinitely many losses on infinitely many tasks can be as statistically easy as minimizing one loss on one task. Along the way, we improve the best known sample complexity guarantee of deterministic omniprediction by a factor of $1/\varepsilon$, and match all other known sample complexity guarantees of omniprediction and multi-group learning. Our key technical ingredient is a nearly lossless reduction from panprediction to a statistically efficient notion of calibration, called step calibration.

Wenqi Fan, Yao Ma, Qing Li et al.

In recent years, Graph Neural Networks (GNNs), which can naturally integrate node information and topological structure, have been demonstrated to be powerful in learning on graph data. These advantages of GNNs provide great potential to advance social recommendation since data in social recommender systems can be represented as user-user social graph and user-item graph; and learning latent factors of users and items is the key. However, building social recommender systems based on GNNs faces challenges. For example, the user-item graph encodes both interactions and their associated opinions; social relations have heterogeneous strengths; users involve in two graphs (e.g., the user-user social graph and the user-item graph). To address the three aforementioned challenges simultaneously, in this paper, we present a novel graph neural network framework (GraphRec) for social recommendations. In particular, we provide a principled approach to jointly capture interactions and opinions in the user-item graph and propose the framework GraphRec, which coherently models two graphs and heterogeneous strengths. Extensive experiments on two real-world datasets demonstrate the effectiveness of the proposed framework GraphRec. Our code is available at \url{https://github.com/wenqifan03/GraphRec-WWW19}

Eric Zhao, Pranjal Awasthi, Sreenivas Gollapudi

Sampling-based search, a simple paradigm for utilizing test-time compute, involves generating multiple candidate responses and selecting the best one -- typically by having models self-verify each response for correctness. In this paper, we study the scaling trends governing sampling-based search. Among our findings is that simply scaling up a minimalist implementation of sampling-based search, using only random sampling and direct self-verification, provides a practical inference method that, for example, elevates the reasoning capabilities of Gemini v1.5 Pro above that of o1-Preview on popular benchmarks. We partially attribute the scalability of sampling-based search to a phenomenon of implicit scaling, where sampling a larger pool of responses in turn improves self-verification accuracy. We further identify two useful principles for improving self-verification capabilities with test-time compute: (1) comparing across responses provides helpful signals about the locations of errors and hallucinations, and (2) different model output styles are useful for different contexts -- chains of thought are useful for reasoning but harder to verify. We also find that, though accurate verification can be elicited, frontier models demonstrate remarkably weak out-of-box verification capabilities and introduce a benchmark to measure progress on these deficiencies.

Ziyang Li, Jiani Huang, Jason Liu et al.

Foundation models have vast potential to enable diverse AI applications. The powerful yet incomplete nature of these models has spurred a wide range of mechanisms to augment them with capabilities such as in-context learning, information retrieval, and code interpreting. We propose Vieira, a declarative framework that unifies these mechanisms in a general solution for programming with foundation models. Vieira follows a probabilistic relational paradigm and treats foundation models as stateless functions with relational inputs and outputs. It supports neuro-symbolic applications by enabling the seamless combination of such models with logic programs, as well as complex, multi-modal applications by streamlining the composition of diverse sub-models. We implement Vieira by extending the Scallop compiler with a foreign interface that supports foundation models as plugins. We implement plugins for 12 foundation models including GPT, CLIP, and SAM. We evaluate Vieira on 9 challenging tasks that span language, vision, and structured and vector databases. Our evaluation shows that programs in Vieira are concise, can incorporate modern foundation models, and have comparable or better accuracy than competitive baselines.

Mingda Qiao, Eric Zhao

Calibration measures quantify how much a forecaster's predictions violates calibration, which requires that forecasts are unbiased conditioning on the forecasted probabilities. Two important desiderata for a calibration measure are its decision-theoretic implications (i.e., downstream decision-makers that best-respond to the forecasts are always no-regret) and its truthfulness (i.e., a forecaster approximately minimizes error by always reporting the true probabilities). Existing measures satisfy at most one of the properties, but not both. We introduce a new calibration measure termed subsampled step calibration, $\mathsf{StepCE}^{\textsf{sub}}$, that is both decision-theoretic and truthful. In particular, on any product distribution, $\mathsf{StepCE}^{\textsf{sub}}$ is truthful up to an $O(1)$ factor whereas prior decision-theoretic calibration measures suffer from an $e^{-Ω(T)}$-$Ω(\sqrt{T})$ truthfulness gap. Moreover, in any smoothed setting where the conditional probability of each event is perturbed by a noise of magnitude $c > 0$, $\mathsf{StepCE}^{\textsf{sub}}$ is truthful up to an $O(\sqrt{\log(1/c)})$ factor, while prior decision-theoretic measures have an $e^{-Ω(T)}$-$Ω(T^{1/3})$ truthfulness gap. We also prove a general impossibility result for truthful decision-theoretic forecasting: any complete and decision-theoretic calibration measure must be discontinuous and non-truthful in the non-smoothed setting.

Naman Agarwal, Pranjal Awasthi, Satyen Kale et al. · deepmind

Stacking, a heuristic technique for training deep residual networks by progressively increasing the number of layers and initializing new layers by copying parameters from older layers, has proven quite successful in improving the efficiency of training deep neural networks. In this paper, we propose a theoretical explanation for the efficacy of stacking: viz., stacking implements a form of Nesterov's accelerated gradient descent. The theory also covers simpler models such as the additive ensembles constructed in boosting methods, and provides an explanation for a similar widely-used practical heuristic for initializing the new classifier in each round of boosting. We also prove that for certain deep linear residual networks, stacking does provide accelerated training, via a new potential function analysis of the Nesterov's accelerated gradient method which allows errors in updates. We conduct proof-of-concept experiments to validate our theory as well.

Eric Zhao, Pranjal Awasthi, Nika Haghtalab

Finetuning provides a scalable and cost-effective means of customizing language models for specific tasks or response styles, with greater reliability than prompting or in-context learning. In contrast, the conventional wisdom is that injecting knowledge via finetuning results in brittle performance and poor generalization. We argue that the dichotomy of "task customization" (e.g., instruction tuning) and "knowledge injection" (e.g., teaching new facts) is a distinction without a difference. We instead identify concrete factors that explain the heterogeneous effectiveness observed with finetuning. To this end, we conduct a large-scale experimental study of finetuning the frontier Gemini v1.5 model family on a spectrum of datasets that are artificially engineered to interpolate between the strengths and failure modes of finetuning. Our findings indicate that question-answer training data formats provide much stronger knowledge generalization than document/article-style training data, numerical information can be harder for finetuning to retain than categorical information, and models struggle to apply finetuned knowledge during multi-step reasoning even when trained on similar examples -- all factors that render "knowledge injection" to be especially difficult, even after controlling for considerations like data augmentation and information volume. On the other hand, our findings also indicate that it is not fundamentally more difficult to finetune information about a real-world event than information about what a model's writing style should be.

Jessica Dai, Nika Haghtalab, Eric Zhao

A canonical desideratum for prediction problems is that performance guarantees should hold not just on average over the population, but also for meaningful subpopulations within the overall population. But what constitutes a meaningful subpopulation? In this work, we take the perspective that relevant subpopulations should be defined with respect to the clusters that naturally emerge from the distribution of individuals for which predictions are being made. In this view, a population refers to a mixture model whose components constitute the relevant subpopulations. We suggest two formalisms for capturing per-subgroup guarantees: first, by attributing each individual to the component from which they were most likely drawn, given their features; and second, by attributing each individual to all components in proportion to their relative likelihood of having been drawn from each component. Using online calibration as a case study, we study a multi-objective algorithm that provides guarantees for each of these formalisms by handling all plausible underlying subpopulation structures simultaneously, and achieve an $O(T^{1/2})$ rate even when the subpopulations are not well-separated. In comparison, the more natural cluster-then-predict approach that first recovers the structure of the subpopulations and then makes predictions suffers from a $O(T^{2/3})$ rate and requires the subpopulations to be separable. Along the way, we prove that providing per-subgroup calibration guarantees for underlying clusters can be easier than learning the clusters: separation between median subgroup features is required for the latter but not the former.

Eric Zhao, Tatjana Chavdarova, Michael Jordan

Variational inequalities (VIs) are a broad class of optimization problems encompassing machine learning problems ranging from standard convex minimization to more complex scenarios like min-max optimization and computing the equilibria of multi-player games. In convex optimization, strong convexity allows for fast statistical learning rates requiring only $Θ(1/ε)$ stochastic first-order oracle calls to find an $ε$-optimal solution, rather than the standard $Θ(1/ε^2)$ calls. This note provides a simple overview of how one can similarly obtain fast $Θ(1/ε)$ rates for learning VIs that satisfy strong monotonicity, a generalization of strong convexity. Specifically, we demonstrate that standard stability-based generalization arguments for convex minimization extend directly to VIs when the domain admits a small covering, or when the operator is integrable and suboptimality is measured by potential functions; such as when finding equilibria in multi-player games.

Emilio Calvano, Nika Haghtalab, Ellen Vitercik et al.

Digital services face a fundamental trade-off in content selection: they must balance the immediate revenue gained from high-reward content against the long-term benefits of maintaining user engagement. Traditional multi-armed bandit models assume that users remain perpetually engaged, failing to capture the possibility that users may disengage when dissatisfied, thereby reducing future revenue potential. In this work, we introduce a model for the content selection problem that explicitly accounts for variable user engagement and disengagement. In our framework, content that maximizes immediate reward is not necessarily optimal in terms of fostering sustained user engagement. Our contributions are twofold. First, we develop computational and statistical methods for offline optimization and online learning of content selection policies. For users whose engagement patterns are defined by $k$ distinct levels, we design a dynamic programming algorithm that computes the exact optimal policy in $O(k^2)$ time. Moreover, we derive no-regret learning guarantees for an online learning setting in which the platform serves a series of users with unknown and potentially adversarial engagement patterns. Second, we introduce the concept of modified demand elasticity which captures how small changes in a user's overall satisfaction affect the platform's ability to secure long-term revenue. This notion generalizes classical demand elasticity by incorporating the dynamics of user re-engagement, thereby revealing key insights into the interplay between engagement and revenue. Notably, our analysis uncovers a counterintuitive phenomenon: although higher friction (i.e., a reduced likelihood of re-engagement) typically lowers overall revenue, it can simultaneously lead to higher user engagement under optimal content selection policies.

Pranjal Awasthi, Nika Haghtalab, Eric Zhao

Multi-distribution learning is a natural generalization of PAC learning to settings with multiple data distributions. There remains a significant gap between the known upper and lower bounds for PAC-learnable classes. In particular, though we understand the sample complexity of learning a VC dimension d class on $k$ distributions to be $O(ε^{-2} \ln(k)(d + k) + \min\{ε^{-1} dk, ε^{-4} \ln(k) d\})$, the best lower bound is $Ω(ε^{-2}(d + k \ln(k)))$. We discuss recent progress on this problem and some hurdles that are fundamental to the use of game dynamics in statistical learning.

Eric Zhao, Alexander R. Trott, Caiming Xiong et al.

We study the problem of training a principal in a multi-agent general-sum game using reinforcement learning (RL). Learning a robust principal policy requires anticipating the worst possible strategic responses of other agents, which is generally NP-hard. However, we show that no-regret dynamics can identify these worst-case responses in poly-time in smooth games. We propose a framework that uses this policy evaluation method for efficiently learning a robust principal policy using RL. This framework can be extended to provide robustness to boundedly rational agents too. Our motivating application is automated mechanism design: we empirically demonstrate our framework learns robust mechanisms in both matrix games and complex spatiotemporal games. In particular, we learn a dynamic tax policy that improves the welfare of a simulated trade-and-barter economy by 15%, even when facing previously unseen boundedly rational RL taxpayers.

Yunjiang Jiang, Yue Shang, Rui Li et al.

Result relevance scoring is critical to e-commerce search user experience. Traditional information retrieval methods focus on keyword matching and hand-crafted or counting-based numeric features, with limited understanding of item semantic relevance. We describe a highly-scalable feed-forward neural model to provide relevance score for (query, item) pairs, using only user query and item title as features, and both user click feedback as well as limited human ratings as labels. Several general enhancements were applied to further optimize eval/test metrics, including Siamese pairwise architecture, random batch negative co-training, and point-wise fine-tuning. We found significant improvement over GBDT baseline as well as several off-the-shelf deep-learning baselines on an independently constructed ratings dataset. The GBDT model relies on 10 times more features. We also present metrics for select subset combinations of techniques mentioned above.

Eric Zhao, Anqi Liu, Animashree Anandkumar et al.

We address the problem of active learning under label shift: when the class proportions of source and target domains differ. We introduce a "medial distribution" to incorporate a tradeoff between importance weighting and class-balanced sampling and propose their combined usage in active learning. Our method is known as Mediated Active Learning under Label Shift (MALLS). It balances the bias from class-balanced sampling and the variance from importance weighting. We prove sample complexity and generalization guarantees for MALLS which show active learning reduces asymptotic sample complexity even under arbitrary label shift. We empirically demonstrate MALLS scales to high-dimensional datasets and can reduce the sample complexity of active learning by 60% in deep active learning tasks.

Yao Ma, Ziyi Guo, Zhaochun Ren et al.

Graphs are essential representations of many real-world data such as social networks. Recent years have witnessed the increasing efforts made to extend the neural network models to graph-structured data. These methods, which are usually known as the graph neural networks, have been applied to advance many graphs related tasks such as reasoning dynamics of the physical system, graph classification, and node classification. Most of the existing graph neural network models have been designed for static graphs, while many real-world graphs are inherently dynamic. For example, social networks are naturally evolving as new users joining and new relations being created. Current graph neural network models cannot utilize the dynamic information in dynamic graphs. However, the dynamic information has been proven to enhance the performance of many graph analytic tasks such as community detection and link prediction. Hence, it is necessary to design dedicated graph neural networks for dynamic graphs. In this paper, we propose DGNN, a new {\bf D}ynamic {\bf G}raph {\bf N}eural {\bf N}etwork model, which can model the dynamic information as the graph evolving. In particular, the proposed framework can keep updating node information by capturing the sequential information of edges (interactions), the time intervals between edges and information propagation coherently. Experimental results on various dynamic graphs demonstrate the effectiveness of the proposed framework.