Model-free Low-Rank Reinforcement Learning via Leveraged Entry-wise Matrix Estimation

• URL: http://arxiv.org/abs/2410.23434v2
• Date: Sun, 10 Nov 2024 07:56:47 GMT
• Title: Model-free Low-Rank Reinforcement Learning via Leveraged Entry-wise Matrix Estimation
• Authors: Stefan Stojanovic, Yassir Jedra, Alexandre Proutiere,
• Abstract summary: We present LoRa-PI (Low-Rank Policy Iteration), a model-free learning algorithm alternating between policy improvement and policy evaluation steps. LoRa-PI learns an $varepsilon$-optimal policy using $widetildeO(S+Aover mathrmpoly (1-gamma)varepsilon2)$ samples where $S$ denotes the number of states (resp. actions) and $gamma$ the discount factor.
• Score: 48.92318828548911
• License:
• Abstract: We consider the problem of learning an $\varepsilon$-optimal policy in controlled dynamical systems with low-rank latent structure. For this problem, we present LoRa-PI (Low-Rank Policy Iteration), a model-free learning algorithm alternating between policy improvement and policy evaluation steps. In the latter, the algorithm estimates the low-rank matrix corresponding to the (state, action) value function of the current policy using the following two-phase procedure. The entries of the matrix are first sampled uniformly at random to estimate, via a spectral method, the leverage scores of its rows and columns. These scores are then used to extract a few important rows and columns whose entries are further sampled. The algorithm exploits these new samples to complete the matrix estimation using a CUR-like method. For this leveraged matrix estimation procedure, we establish entry-wise guarantees that remarkably, do not depend on the coherence of the matrix but only on its spikiness. These guarantees imply that LoRa-PI learns an $\varepsilon$-optimal policy using $\widetilde{O}({S+A\over \mathrm{poly}(1-\gamma)\varepsilon^2})$ samples where $S$ (resp. $A$) denotes the number of states (resp. actions) and $\gamma$ the discount factor. Our algorithm achieves this order-optimal (in $S$, $A$ and $\varepsilon$) sample complexity under milder conditions than those assumed in previously proposed approaches.

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