# Policy Optimization as Online Learning with Mediator Feedback

arXiv: https://arxiv.org/abs/2012.08225 · HTML: https://mlsanity.com/paper/2012.08225/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2020.

## Built on by (most cited first, 4 of 4)

- [Reward-Free Policy Space Compression for Reinforcement Learning](https://mlsanity.com/paper/2202.11079/) (2022)
- [Information Capacity Regret Bounds for Bandits with Mediator Feedback](https://mlsanity.com/paper/2402.10282/) (2024)
- [Information-Theoretic Regret Bounds for Bandits with Fixed Expert Advice](https://mlsanity.com/paper/2303.08102/) (2023)
- [Pure Exploration under Mediators' Feedback](https://mlsanity.com/paper/2308.15552/) (2023)

## Abstract (arXiv)

Policy Optimization (PO) is a widely used approach to address continuous control tasks. In this paper, we introduce the notion of mediator feedback that frames PO as an online learning problem over the policy space. The additional available information, compared to the standard bandit feedback, allows reusing samples generated by one policy to estimate the performance of other policies. Based on this observation, we propose an algorithm, RANDomized-exploration policy Optimization via Multiple Importance Sampling with Truncation (RANDOMIST), for regret minimization in PO, that employs a randomized exploration strategy, differently from the existing optimistic approaches. When the policy space is finite, we show that under certain circumstances, it is possible to achieve constant regret, while always enjoying logarithmic regret. We also derive problem-dependent regret lower bounds. Then, we extend RANDOMIST to compact policy spaces. Finally, we provide numerical simulations on finite and compact policy spaces, in comparison with PO and bandit baselines.