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Near-Optimal Regret in Linear MDPs with Aggregate Bandit Feedback
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Extends aggregate-bandit-feedback RL to linear MDPs and gives two regret algorithms (RE-LSVI optimistic value-based and REPO policy optimization) built on a Gaussian reward-perturbation ensemble with hedging.
Problem
Reinforcement learning when only the episode's total reward is observed at episode end (aggregate bandit feedback), under linear MDP function approximation, where prior work was limited to tabular settings.
Approach
Optimism is obtained by drawing m i.i.d. Gaussian perturbations of the aggregate-reward estimate and following the ensemble member with the highest initial value (RE-LSVI), with a loose symmetric clipping to avoid bias; REPO extends this to policy optimization using multiplicative-weights hedging over the ensemble and an indicator on known states.
Key results
- RE-LSVI achieves regret O(sqrt(d^5 H^7 K)) up to log factors with high probability.
- REPO achieves regret O(sqrt(d^5 H^9 K)) up to log factors, the first policy optimization algorithm for aggregate feedback.
- Ensemble of m ≈ log(K/δ) Gaussian perturbations ensures at least one member is optimistic with high probability.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use RE-LSVI instead of REPO | Regret minimization in linear MDPs with aggregate bandit feedback · Linear MDPs with aggregate bandit feedback | regret bound dependence on H: RE-LSVI: \tilde{O}(\sqrt{ d^5 H^7 K}); REPO: O\brk*{\sqrt{ d^5 H^9 K \log^9 (dH \abs{\mathcal{A}} K / \delta)}} | Helped |
| Use an ensemble of m independent Gaussian perturbations and select the member with maximal value, rather than sampling noise only once | RE-LSVI · Linear MDPs with aggregate bandit feedback | probability of obtaining an optimistic value estimate: m \approx \log(K/\delta); \ge 1 - \delta | Helped |
| Use an epoch-fixed reward perturbation rather than drawing a new perturbation each episode | REPO · Linear MDPs with aggregate bandit feedback | optimistic guarantees | Helped |
Limitations
- Regret bounds carry large polynomial and log factors in d and H.
- REPO's analysis requires a reward-free warm-up of about sqrt(K) episodes and epoch scheduling.
- The tabular REPO variant relies on valid (nonnegative) estimated dynamics, which does not carry over to linear MDPs.
Experimental setup
Metrics: regret
Baselines: Tabular RL-ABF algorithms (Cassel et al. 2024 style) Preference-based RL randomized linear MDP algorithm (concurrent work)
Builds on: LSVI-UCB UCBVI-TS Linear MDP Multiplicative weights
Closest papers by meaning
- Near-optimal Regret Using Policy Optimization in Online MDPs with Aggregate Bandit Feedback (ICML 2025 · similarity 0.91)
- Towards Optimal Regret in Adversarial Linear MDPs with Bandit Feedback (ICLR 2024 · similarity 0.89)
- Achieving Constant Regret in Linear Markov Decision Processes (NeurIPS 2024 · similarity 0.88)
- Minimax Optimal Regret Bound for Reinforcement Learning with Trajectory Feedback (ICML 2025 · similarity 0.88)
- Rate-Optimal Policy Optimization for Linear Markov Decision Processes (ICML 2024 · similarity 0.88)
- Hybrid Reinforcement Learning Breaks Sample Size Barriers In Linear MDPs (NeurIPS 2024 · similarity 0.88)
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