# Near-optimal Regret Using Policy Optimization in Online MDPs with Aggregate Bandit Feedback

arXiv: https://arxiv.org/abs/2502.04004 · HTML: https://mlsanity.com/paper/2502.04004/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2025.

## Built on by (most cited first, 6 of 6)

- [Do We Need to Verify Step by Step? Rethinking Process Supervision from a Theoretical Perspective](https://mlsanity.com/paper/2502.10581/) (2025)
- [Outcome-Based Online Reinforcement Learning: Algorithms and Fundamental Limits](https://mlsanity.com/paper/2505.20268/) (2025)
- [Adapting to Stochastic and Adversarial Losses in Episodic MDPs with Aggregate Bandit Feedback](https://mlsanity.com/paper/2510.17103/) (2025)
- [Optimal Regret for Policy Optimization in Contextual Bandits](https://mlsanity.com/paper/2602.13700/) (2026)
- [Near-Optimal Regret for Policy Optimization in Contextual MDPs with General Offline Function Approximation](https://mlsanity.com/paper/2602.13706/) (2026)
- [When Does Trajectory-Level Supervision Permit Efficient Offline Reinforcement Learning?](https://mlsanity.com/paper/2606.18531/) (2026)

## Abstract (arXiv)

We study online finite-horizon Markov Decision Processes with adversarially changing loss and aggregate bandit feedback (a.k.a full-bandit). Under this type of feedback, the agent observes only the total loss incurred over the entire trajectory, rather than the individual losses at each intermediate step within the trajectory. We introduce the first Policy Optimization algorithms for this setting. In the known-dynamics case, we achieve the first textitoptimal regret bound of tilde Theta(H2√SAK), where K is the number of episodes, H is the episode horizon, S is the number of states, and A is the number of actions. In the unknown dynamics case we establish regret bound of tilde O(H3 S √AK), significantly improving the best known result by a factor of H2 S5 A2.