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Reinforcement Learning in Linear MDPs: Constant Regret and Representation Selection
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a UNISOFT representation with ELEANOR | ELEANOR on Bellman closure MDPs · Bellman closure MDPs | regret: \wt{O}(\sqrt{d^2H^3T}) -> H^{3/2}d\sqrt{\wb\tau\log\frac{\wb\tau}{\delta}} | Helped |
| Use a UNISOFT representation with LSVI-UCB | LSVI-UCB on low-rank MDPs · Low-rank MDPs | regret: \wt{O}(\sqrt{d^3H^3T}) -> \frac{d^3 H^5}{\Delta_{\min}} \log \big(dH^2 \wb\kappa / \delta\big) | Helped |
| Select the tightest optimistic estimate across supplied representations | LSVI-LEADER on low-rank MDPs · Low-rank MDPs with a set of representations | regret: R(K) \leq \min_{z\in\mathcal{Z}}\wt{R}(K, z, \{\beta_k\}) | Helped |
| Mix representations across states and actions when the family is UNISOFT-mixing | LSVI-LEADER on low-rank MDPs · Low-rank MDPs with UNISOFT-mixing representations | regret: R(K) \leq \min_{z\in\mathcal{Z}}\wt{R}\big( \wt{\kappa}, z, \{\beta_k\} \big) | Helped |
| Use a non-UNISOFT representation | Any algorithm consistent across MDPs with linear rewards · MDPs with linear rewards and arbitrary dynamics | regret | Hurt |
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