arXiv subjects

Mehryar Mohri

Publications and source records attributed to Mehryar Mohri.

At least 73 records · Page 4Linked to original sources

arXiv2021

Adapting to Misspecification in Contextual Bandits

A major research direction in contextual bandits is to develop algorithms that are computationally efficient, yet support flexible, general-purpose function approximation. Algorithms based on modeling rewards have shown strong empirical performance, but typically require a well-specified model, and can fail when this assumption does not hold. Can we design algorithms that are efficient and flexible, yet degrade gracefully in the face of model misspecification? We introduce a new family of oracle-efficient algorithms for $\varepsilon$-misspecified contextual bandits that adapt to unknown model misspecification -- both for finite and infinite action settings. Given access to an online oracle for square loss regression, our algorithm attains optimal regret and -- in particular -- optimal dependence on the misspecification level, with no prior knowledge. Specializing to linear contextual bandits with infinite actions in $d$ dimensions, we obtain the first algorithm that achieves the optimal $O(d\sqrt{T} + \varepsilon\sqrt{d}T)$ regret bound for unknown misspecification level $\varepsilon$. On a conceptual level, our results are enabled by a new optimization-based perspective on the regression oracle reduction framework of Foster and Rakhlin, which we anticipate will find broader use.

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arXiv2021

Agnostic Reinforcement Learning with Low-Rank MDPs and Rich Observations

There have been many recent advances on provably efficient Reinforcement Learning (RL) in problems with rich observation spaces. However, all these works share a strong realizability assumption about the optimal value function of the true MDP. Such realizability assumptions are often too strong to hold in practice. In this work, we consider the more realistic setting of agnostic RL with rich observation spaces and a fixed class of policies $Π$ that may not contain any near-optimal policy. We provide an algorithm for this setting whose error is bounded in terms of the rank $d$ of the underlying MDP. Specifically, our algorithm enjoys a sample complexity bound of $\widetilde{O}\left((H^{4d} K^{3d} \log |Π|)/ε^2\right)$ where $H$ is the length of episodes, $K$ is the number of actions and $ε>0$ is the desired sub-optimality. We also provide a nearly matching lower bound for this agnostic setting that shows that the exponential dependence on rank is unavoidable, without further assumptions.

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arXiv2021

Communication-Efficient Agnostic Federated Averaging

In distributed learning settings such as federated learning, the training algorithm can be potentially biased towards different clients. Mohri et al. (2019) proposed a domain-agnostic learning algorithm, where the model is optimized for any target distribution formed by a mixture of the client distributions in order to overcome this bias. They further proposed an algorithm for the cross-silo federated learning setting, where the number of clients is small. We consider this problem in the cross-device setting, where the number of clients is much larger. We propose a communication-efficient distributed algorithm called Agnostic Federated Averaging (or AgnosticFedAvg) to minimize the domain-agnostic objective proposed in Mohri et al. (2019), which is amenable to other private mechanisms such as secure aggregation. We highlight two types of naturally occurring domains in federated learning and argue that AgnosticFedAvg performs well on both. To demonstrate the practical effectiveness of AgnosticFedAvg, we report positive results for large-scale language modeling tasks in both simulation and live experiments, where the latter involves training language models for Spanish virtual keyboard for millions of user devices.

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arXiv2021

Mime: Mimicking Centralized Stochastic Algorithms in Federated Learning

Federated learning (FL) is a challenging setting for optimization due to the heterogeneity of the data across different clients which gives rise to the client drift phenomenon. In fact, obtaining an algorithm for FL which is uniformly better than simple centralized training has been a major open problem thus far. In this work, we propose a general algorithmic framework, Mime, which i) mitigates client drift and ii) adapts arbitrary centralized optimization algorithms such as momentum and Adam to the cross-device federated learning setting. Mime uses a combination of control-variates and server-level statistics (e.g. momentum) at every client-update step to ensure that each local update mimics that of the centralized method run on iid data. We prove a reduction result showing that Mime can translate the convergence of a generic algorithm in the centralized setting into convergence in the federated setting. Further, we show that when combined with momentum based variance reduction, Mime is provably faster than any centralized method--the first such result. We also perform a thorough experimental exploration of Mime's performance on real world datasets.

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arXiv2021

A Finer Calibration Analysis for Adversarial Robustness

We present a more general analysis of $H$-calibration for adversarially robust classification. By adopting a finer definition of calibration, we can cover settings beyond the restricted hypothesis sets studied in previous work. In particular, our results hold for most common hypothesis sets used in machine learning. We both fix some previous calibration results (Bao et al., 2020) and generalize others (Awasthi et al., 2021). Moreover, our calibration results, combined with the previous study of consistency by Awasthi et al. (2021), also lead to more general $H$-consistency results covering common hypothesis sets.

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arXiv2021

Calibration and Consistency of Adversarial Surrogate Losses

Adversarial robustness is an increasingly critical property of classifiers in applications. The design of robust algorithms relies on surrogate losses since the optimization of the adversarial loss with most hypothesis sets is NP-hard. But which surrogate losses should be used and when do they benefit from theoretical guarantees? We present an extensive study of this question, including a detailed analysis of the H-calibration and H-consistency of adversarial surrogate losses. We show that, under some general assumptions, convex loss functions, or the supremum-based convex losses often used in applications, are not H-calibrated for important hypothesis sets such as generalized linear models or one-layer neural networks. We then give a characterization of H-calibration and prove that some surrogate losses are indeed H-calibrated for the adversarial loss, with these hypothesis sets. Next, we show that H-calibration is not sufficient to guarantee consistency and prove that, in the absence of any distributional assumption, no continuous surrogate loss is consistent in the adversarial setting. This, in particular, proves that a claim presented in a COLT 2020 publication is inaccurate. (Calibration results there are correct modulo subtle definition differences, but the consistency claim does not hold.) Next, we identify natural conditions under which some surrogate losses that we describe in detail are H-consistent for hypothesis sets such as generalized linear models and one-layer neural networks. We also report a series of empirical results with simulated data, which show that many H-calibrated surrogate losses are indeed not H-consistent, and validate our theoretical assumptions.

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arXiv2021

SCAFFOLD: Stochastic Controlled Averaging for Federated Learning

Federated Averaging (FedAvg) has emerged as the algorithm of choice for federated learning due to its simplicity and low communication cost. However, in spite of recent research efforts, its performance is not fully understood. We obtain tight convergence rates for FedAvg and prove that it suffers from `client-drift' when the data is heterogeneous (non-iid), resulting in unstable and slow convergence. As a solution, we propose a new algorithm (SCAFFOLD) which uses control variates (variance reduction) to correct for the `client-drift' in its local updates. We prove that SCAFFOLD requires significantly fewer communication rounds and is not affected by data heterogeneity or client sampling. Further, we show that (for quadratics) SCAFFOLD can take advantage of similarity in the client's data yielding even faster convergence. The latter is the first result to quantify the usefulness of local-steps in distributed optimization.

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arXiv2021

Advances and Open Problems in Federated Learning

Federated learning (FL) is a machine learning setting where many clients (e.g. mobile devices or whole organizations) collaboratively train a model under the orchestration of a central server (e.g. service provider), while keeping the training data decentralized. FL embodies the principles of focused data collection and minimization, and can mitigate many of the systemic privacy risks and costs resulting from traditional, centralized machine learning and data science approaches. Motivated by the explosive growth in FL research, this paper discusses recent advances and presents an extensive collection of open problems and challenges.

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arXiv2021

Corralling Stochastic Bandit Algorithms

We study the problem of corralling stochastic bandit algorithms, that is combining multiple bandit algorithms designed for a stochastic environment, with the goal of devising a corralling algorithm that performs almost as well as the best base algorithm. We give two general algorithms for this setting, which we show benefit from favorable regret guarantees. We show that the regret of the corralling algorithms is no worse than that of the best algorithm containing the arm with the highest reward, and depends on the gap between the highest reward and other rewards.

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arXiv2021

A Discriminative Technique for Multiple-Source Adaptation

We present a new discriminative technique for the multiple-source adaptation, MSA, problem. Unlike previous work, which relies on density estimation for each source domain, our solution only requires conditional probabilities that can easily be accurately estimated from unlabeled data from the source domains. We give a detailed analysis of our new technique, including general guarantees based on Rényi divergences, and learning bounds when conditional Maxent is used for estimating conditional probabilities for a point to belong to a source domain. We show that these guarantees compare favorably to those that can be derived for the generative solution, using kernel density estimation. Our experiments with real-world applications further demonstrate that our new discriminative MSA algorithm outperforms the previous generative solution as well as other domain adaptation baselines.

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arXiv2020

A Theory of Multiple-Source Adaptation with Limited Target Labeled Data

We present a theoretical and algorithmic study of the multiple-source domain adaptation problem in the common scenario where the learner has access only to a limited amount of labeled target data, but where the learner has at disposal a large amount of labeled data from multiple source domains. We show that a new family of algorithms based on model selection ideas benefits from very favorable guarantees in this scenario and discuss some theoretical obstacles affecting some alternative techniques. We also report the results of several experiments with our algorithms that demonstrate their practical effectiveness.

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arXiv2020

Relative Deviation Margin Bounds

We present a series of new and more favorable margin-based learning guarantees that depend on the empirical margin loss of a predictor. We give two types of learning bounds, both distribution-dependent and valid for general families, in terms of the Rademacher complexity or the empirical $\ell_\infty$ covering number of the hypothesis set used. Furthermore, using our relative deviation margin bounds, we derive distribution-dependent generalization bounds for unbounded loss functions under the assumption of a finite moment. We also briefly highlight several applications of these bounds and discuss their connection with existing results.

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arXiv2020

Hypothesis Set Stability and Generalization

We present a study of generalization for data-dependent hypothesis sets. We give a general learning guarantee for data-dependent hypothesis sets based on a notion of transductive Rademacher complexity. Our main result is a generalization bound for data-dependent hypothesis sets expressed in terms of a notion of hypothesis set stability and a notion of Rademacher complexity for data-dependent hypothesis sets that we introduce. This bound admits as special cases both standard Rademacher complexity bounds and algorithm-dependent uniform stability bounds. We also illustrate the use of these learning bounds in the analysis of several scenarios.

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arXiv2020

Discrepancy-Based Algorithms for Non-Stationary Rested Bandits

We study the multi-armed bandit problem where the rewards are realizations of general non-stationary stochastic processes, a setting that generalizes many existing lines of work and analyses. In particular, we present a theoretical analysis and derive regret guarantees for rested bandits in which the reward distribution of each arm changes only when we pull that arm. Remarkably, our regret bounds are logarithmic in the number of rounds under several natural conditions. We introduce a new algorithm based on classical UCB ideas combined with the notion of weighted discrepancy, a useful tool for measuring the non-stationarity of a stochastic process. We show that the notion of discrepancy can be used to design very general algorithms and a unified framework for the analysis of multi-armed rested bandit problems with non-stationary rewards. In particular, we show that we can recover the regret guarantees of many specific instances of bandit problems with non-stationary rewards that have been studied in the literature. We also provide experiments demonstrating that our algorithms can enjoy a significant improvement in practice compared to standard benchmarks.

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arXiv2020

Beyond Individual and Group Fairness

We present a new data-driven model of fairness that, unlike existing static definitions of individual or group fairness is guided by the unfairness complaints received by the system. Our model supports multiple fairness criteria and takes into account their potential incompatibilities. We consider both a stochastic and an adversarial setting of our model. In the stochastic setting, we show that our framework can be naturally cast as a Markov Decision Process with stochastic losses, for which we give efficient vanishing regret algorithmic solutions. In the adversarial setting, we design efficient algorithms with competitive ratio guarantees. We also report the results of experiments with our algorithms and the stochastic framework on artificial datasets, to demonstrate their effectiveness empirically.

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arXiv2020

On the Rademacher Complexity of Linear Hypothesis Sets

Linear predictors form a rich class of hypotheses used in a variety of learning algorithms. We present a tight analysis of the empirical Rademacher complexity of the family of linear hypothesis classes with weight vectors bounded in $\ell_p$-norm for any $p \geq 1$. This provides a tight analysis of generalization using these hypothesis sets and helps derive sharp data-dependent learning guarantees. We give both upper and lower bounds on the Rademacher complexity of these families and show that our bounds improve upon or match existing bounds, which are known only for $1 \leq p \leq 2$.

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arXiv2020

Three Approaches for Personalization with Applications to Federated Learning

The standard objective in machine learning is to train a single model for all users. However, in many learning scenarios, such as cloud computing and federated learning, it is possible to learn a personalized model per user. In this work, we present a systematic learning-theoretic study of personalization. We propose and analyze three approaches: user clustering, data interpolation, and model interpolation. For all three approaches, we provide learning-theoretic guarantees and efficient algorithms for which we also demonstrate the performance empirically. All of our algorithms are model-agnostic and work for any hypothesis class.

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arXiv2020

Reinforcement Learning with Feedback Graphs

We study episodic reinforcement learning in Markov decision processes when the agent receives additional feedback per step in the form of several transition observations. Such additional observations are available in a range of tasks through extended sensors or prior knowledge about the environment (e.g., when certain actions yield similar outcome). We formalize this setting using a feedback graph over state-action pairs and show that model-based algorithms can leverage the additional feedback for more sample-efficient learning. We give a regret bound that, ignoring logarithmic factors and lower-order terms, depends only on the size of the maximum acyclic subgraph of the feedback graph, in contrast with a polynomial dependency on the number of states and actions in the absence of a feedback graph. Finally, we highlight challenges when leveraging a small dominating set of the feedback graph as compared to the bandit setting and propose a new algorithm that can use knowledge of such a dominating set for more sample-efficient learning of a near-optimal policy.

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