Regret Minimization via Saddle Point Optimization
<|reference_start|>Regret Minimization via Saddle Point Optimization: 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.<|reference_end|>
@article{kirschner2024regret,
    title={Regret Minimization via Saddle Point Optimization},
    author={Johannes Kirschner, Seyed Alireza Bakhtiari, Kushagra Chandak,
  Volodymyr Tkachuk, Csaba Szepesv'ari},
    journal={arXiv preprint arXiv:2403.10379},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.10379},
    primaryClass={cs.LG}
}