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Mark Squillante

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4 papers

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NeurIPS Conference 2022 Conference Paper

A Stochastic Linearized Augmented Lagrangian Method for Decentralized Bilevel Optimization

Songtao Lu
Siliang Zeng
Xiaodong Cui
Mark Squillante
Lior Horesh
Brian Kingsbury
Jia Liu
Mingyi Hong

Bilevel optimization has been shown to be a powerful framework for formulating multi-task machine learning problems, e. g. , reinforcement learning (RL) and meta-learning, where the decision variables are coupled in both levels of the minimization problems. In practice, the learning tasks would be located at different computing resource environments, and thus there is a need for deploying a decentralized training framework to implement multi-agent and multi-task learning. We develop a stochastic linearized augmented Lagrangian method (SLAM) for solving general nonconvex bilevel optimization problems over a graph, where both upper and lower optimization variables are able to achieve a consensus. We also establish that the theoretical convergence rate of the proposed SLAM to the Karush-Kuhn-Tucker (KKT) points of this class of problems is on the same order as the one achieved by the classical distributed stochastic gradient descent for only single-level nonconvex minimization problems. Numerical results tested on multi-agent RL problems showcase the superiority of SLAM compared with the benchmarks.

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NeurIPS Conference 2021 Conference Paper

Efficient Generalization with Distributionally Robust Learning

Soumyadip Ghosh
Mark Squillante
Ebisa Wollega

Distributionally robust learning (DRL) is increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difﬁcult to solve. We provide a new stochastic gradient descent algorithm to efﬁciently solve this DRL formulation. Our approach applies gradient descent to the outer minimization formulation and estimates the gradient of the inner maximization based on a sample average approximation. The latter uses a subset of the data sampled without replacement in each iteration, progressively increasing the subset size to ensure convergence. We rigorously establish convergence to a near-optimal solution under standard regularity assumptions and, for strongly convex losses, match the best known $O(\epsilon{ −1})$ rate of convergence up to a known threshold. Empirical results demonstrate the signiﬁcant beneﬁts of our approach over previous work in improving learning for model generalization.

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NeurIPS Conference 2020 Conference Paper

Quantifying the Empirical Wasserstein Distance to a Set of Measures: Beating the Curse of Dimensionality

Nian Si
Jose Blanchet
Soumyadip Ghosh
Mark Squillante

We consider the problem of estimating the Wasserstein distance between the empirical measure and a set of probability measures whose expectations over a class of functions (hypothesis class) are constrained. If this class is sufficiently rich to characterize a particular distribution (e. g. , all Lipschitz functions), then our formulation recovers the Wasserstein distance to such a distribution. We establish a strong duality result that generalizes the celebrated Kantorovich-Rubinstein duality. We also show that our formulation can be used to beat the curse of dimensionality, which is well known to affect the rates of statistical convergence of the empirical Wasserstein distance. In particular, examples of infinite-dimensional hypothesis classes are presented, informed by a complex correlation structure, for which it is shown that the empirical Wasserstein distance to such classes converges to zero at the standard parametric rate. Our formulation provides insights that help clarify why, despite the curse of dimensionality, the Wasserstein distance enjoys favorable empirical performance across a wide range of statistical applications.

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NeurIPS Conference 2019 Conference Paper

A Family of Robust Stochastic Operators for Reinforcement Learning

Yingdong Lu
Mark Squillante
Chai Wah Wu

We consider a new family of stochastic operators for reinforcement learning with the goal of alleviating negative effects and becoming more robust to approximation or estimation errors. Various theoretical results are established, which include showing that our family of operators preserve optimality and increase the action gap in a stochastic sense. Our empirical results illustrate the strong benefits of our robust stochastic operators, significantly outperforming the classical Bellman operator and recently proposed operators.

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