Research map / Reinforcement learning / MDPs and planning
Quantum algorithms for reinforcement learning with a generative model
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use quantum mean estimation with variance reduction and total-variance control | SolveMdpI for q* · q* estimation | query complexity: \frac{SA\Gamma^3}{\epsilon^2} -> \frac{SA\Gamma^{1.5}}{\epsilon} | Helped |
| Use quantum mean estimation with variance reduction and total-variance control | SolveMdpI for v* and π* · v* and π* estimation | query complexity: \frac{SA\Gamma^3}{\epsilon^2} -> \frac{SA\Gamma^{1.5}}{\epsilon} | Helped |
| Use quantum maximum finding over actions | SolveMdpII for v* and π* · v* and π* estimation | query complexity dependence on action count A: The paper states a quadratic speedup in A; the table gives \frac{SA\Gamma^{1.5}}{\epsilon} and \frac{S\sqrt{A}\Gamma^{3} | Helped |
| Use quantum maximum finding instead of variance reduction and total-variance techniques | Value and policy estimation · v* and π* estimation | dependence on effective horizon Γ: \frac{SA\Gamma^{1.5}}{\epsilon} -> \frac{S\sqrt{A}\Gamma^{3}}{\epsilon} | Hurt |
| Apply the total-variance technique in the quantum algorithm | SolveMdpI · q*, v*, and π* estimation | query complexity dependence on Γ and ε: The paper gives SolveMdpI complexity \widetilde{O}(SA\Gamma^{1.5}/\epsilon) in its main-results discussion, for \epsilon | Helped |
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