Gap-Dependent Bounds for Nearly Minimax Optimal Reinforcement Learning with Linear Function Approximation

A team of researchers including Haochen Zhang has published a significant theoretical advance in reinforcement learning (RL), providing the first gap-dependent performance guarantees for algorithms that achieve nearly minimax-optimal worst-case regret. The paper focuses on LSVI-UCB++, an algorithm known for its optimal worst-case performance bound of Õ(d√(H³K)), where d is feature dimension, H is horizon length, and K is episodes. Prior gap-dependent analyses couldn't be applied to such minimax-optimal algorithms, creating a theoretical gap between worst-case and instance-specific performance understanding. This work bridges that gap by showing LSVI-UCB++ also enjoys improved, gap-dependent regret bounds that scale better with both d and H compared to previous results.

Beyond the single-agent analysis, the researchers leveraged LSVI-UCB++'s low policy-switching property to create a concurrent variant for multi-agent reinforcement learning. This enables efficient parallel exploration where multiple agents can learn simultaneously without interfering with each other's progress. The team established the first gap-dependent sample complexity upper bound for online multi-agent RL with linear function approximation, demonstrating that their approach achieves linear speedup—meaning adding more agents proportionally reduces the total samples needed. This theoretical foundation could accelerate development of more sample-efficient AI agents for complex real-world tasks where parallel computation is available, moving RL theory closer to practical large-scale deployment.