Regret Minimization via Saddle Point Optimization

Fuente: arXiv
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Main Authors: Kirschner, Johannes, Bakhtiari, Seyed Alireza, Chandak, Kushagra, Tkachuk, Volodymyr, Szepesvári, Csaba
Format: Preprint
Published: 2024
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author Kirschner, Johannes
Bakhtiari, Seyed Alireza
Chandak, Kushagra
Tkachuk, Volodymyr
Szepesvári, Csaba
author_facet Kirschner, Johannes
Bakhtiari, Seyed Alireza
Chandak, Kushagra
Tkachuk, Volodymyr
Szepesvári, Csaba
contents A long line of works characterizes the sample complexity of regret minimization in sequential decision-making by min-max programs. In the corresponding saddle-point game, the min-player optimizes the sampling distribution against an adversarial max-player that chooses confusing models leading to large regret. The most recent instantiation of this idea is the decision-estimation coefficient (DEC), which was shown to provide nearly tight lower and upper bounds on the worst-case expected regret in structured bandits and reinforcement learning. By re-parametrizing the offset DEC with the confidence radius and solving the corresponding min-max program, we derive an anytime variant of the Estimation-To-Decisions (E2D) algorithm. Importantly, the algorithm optimizes the exploration-exploitation trade-off online instead of via the analysis. Our formulation leads to a practical algorithm for finite model classes and linear feedback models. We further point out connections to the information ratio, decoupling coefficient and PAC-DEC, and numerically evaluate the performance of E2D on simple examples.
format Preprint
id arxiv_https___arxiv_org_abs_2403_10379
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Regret Minimization via Saddle Point Optimization
Kirschner, Johannes
Bakhtiari, Seyed Alireza
Chandak, Kushagra
Tkachuk, Volodymyr
Szepesvári, Csaba
Machine Learning
A long line of works characterizes the sample complexity of regret minimization in sequential decision-making by min-max programs. In the corresponding saddle-point game, the min-player optimizes the sampling distribution against an adversarial max-player that chooses confusing models leading to large regret. The most recent instantiation of this idea is the decision-estimation coefficient (DEC), which was shown to provide nearly tight lower and upper bounds on the worst-case expected regret in structured bandits and reinforcement learning. By re-parametrizing the offset DEC with the confidence radius and solving the corresponding min-max program, we derive an anytime variant of the Estimation-To-Decisions (E2D) algorithm. Importantly, the algorithm optimizes the exploration-exploitation trade-off online instead of via the analysis. Our formulation leads to a practical algorithm for finite model classes and linear feedback models. We further point out connections to the information ratio, decoupling coefficient and PAC-DEC, and numerically evaluate the performance of E2D on simple examples.
title Regret Minimization via Saddle Point Optimization
topic Machine Learning
url https://arxiv.org/abs/2403.10379