Pith. sign in

REVIEW 9 cited by

Variance-reduced Q-learning is minimax optimal

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1906.04697 v2 pith:ERVNCQVY submitted 2019-06-11 cs.LG math.OCstat.ML

Variance-reduced Q-learning is minimax optimal

classification cs.LG math.OCstat.ML
keywords mathcalgammalearningleftrightcomplexitydiscountepsilon
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original abstract

We introduce and analyze a form of variance-reduced $Q$-learning. For $\gamma$-discounted MDPs with finite state space $\mathcal{X}$ and action space $\mathcal{U}$, we prove that it yields an $\epsilon$-accurate estimate of the optimal $Q$-function in the $\ell_\infty$-norm using $\mathcal{O} \left(\left(\frac{D}{ \epsilon^2 (1-\gamma)^3} \right) \; \log \left( \frac{D}{(1-\gamma)} \right) \right)$ samples, where $D = |\mathcal{X}| \times |\mathcal{U}|$. This guarantee matches known minimax lower bounds up to a logarithmic factor in the discount complexity. In contrast, our past work shows that ordinary $Q$-learning has worst-case quartic scaling in the discount complexity.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Achieving $\epsilon^{-2}$ Sample Complexity for Single-Loop Actor-Critic under Minimal Assumptions

    cs.LG 2026-05 unverdicted novelty 8.0

    Single-loop actor-critic achieves the first Õ(ε^{-2}) sample complexity for ε-optimal policies under minimal irreducibility assumptions.

  2. Minimax PAC Bounds for Learning in Exogenous Contextual MDPs

    stat.ML 2026-06 unverdicted novelty 7.0

    Derives |Z|-free minimax PAC bounds for policy evaluation and best-policy extraction in exogenous contextual tabular MDPs under oracle access regimes.

  3. Gaussian Approximation for Asynchronous Q-learning

    stat.ML 2026-04 unverdicted novelty 7.0

    Derived rates of order up to n^{-1/6} log^4(n S A) for the high-dimensional CLT of averaged asynchronous Q-learning iterates, plus a general martingale-difference CLT.

  4. A Minimal-Assumption Analysis of Q-Learning with Time-Varying Policies

    cs.LG 2025-10 unverdicted novelty 7.0

    Establishes last-iterate convergence rates for on-policy Q-learning under minimal irreducibility assumptions, with sample complexity O(1/ξ²) matching off-policy up to exploration factors.

  5. From Set Convergence to Pointwise Convergence: Finite-Time Guarantees for Average-Reward Q-Learning with Adaptive Stepsizes

    cs.LG 2025-04 unverdicted novelty 7.0

    Establishes Õ(1/k) mean-square last-iterate convergence for asynchronous average-reward Q-learning with adaptive stepsizes and proves adaptivity is necessary.

  6. Stationary Robust Mean-Field Games under Model Mismatches

    cs.LG 2026-06 unverdicted novelty 6.0

    Develops infinite-horizon stationary robust mean-field games incorporating distributional uncertainty, proves equilibrium existence via fixed-point on contractive Bellman operator, gives convergent algorithm, and deri...

  7. Randomization for Faster Exact Optimization of Discounted Markov Decision Processes

    cs.DS 2026-06 unverdicted novelty 6.0

    Faster deterministic and randomized algorithms for exact DMDP optimization via reductions to policy evaluation and approximate solving.

  8. On Gaussian approximation for entropy-regularized Q-learning with function approximation

    stat.ML 2026-05 unverdicted novelty 5.0

    Establishes n^{-1/4} Gaussian approximation in convex distance for averaged entropy-regularized Q-learning with linear function approximation and polynomial stepsizes.

  9. Mathematical methods of reinforcement learning

    math.OC 2026-07 accept

    A survey unifying the operator-theoretic, probabilistic, and optimization-based mathematical structures underlying modern reinforcement learning algorithms.