We study model-free reinforcement learning (RL) algorithms for infinite-horizon average-reward Markov decision process (MDP), which is more appropriate for applications that involve continuing operations not divided into episodes. In contrast to episodic/discounted MDPs, theoretical understanding of model-free RL algorithms is relatively inadequate for the average-reward setting. In this paper, we consider both the online setting and the setting with access to a simulator. We develop computationally efficient model-free algorithms that achieve sharper guarantees on regret/sample complexity compared with existing results. In the online setting, we design an algorithm, UCB-AVG, based on an optimistic variant of variance-reduced Q-learning. We show that UCB-AVG achieves a regret bound $\widetilde{O}(S^5A^2sp(h^*)\sqrt{T})$ after $T$ steps, where $S\times A$ is the size of state-action space, and $sp(h^*)$ the span of the optimal bias function. Our result provides the first computationally efficient model-free algorithm that achieves the optimal dependence in $T$ (up to log factors) for weakly communicating MDPs, which is necessary for low regret. In contrast, prior results either are suboptimal in $T$ or require strong assumptions of ergodicity or uniformly mixing of MDPs. In the simulator setting, we adapt the idea of UCB-AVG to develop a model-free algorithm that finds an $\epsilon$-optimal policy with sample complexity $\widetilde{O}(SAsp^2(h^*)\epsilon^{-2} + S^2Asp(h^*)\epsilon^{-1}).$ This sample complexity is near-optimal for weakly communicating MDPs, in view of the minimax lower bound $\Omega(SAsp(^*)\epsilon^{-2})$. Existing work mainly focuses on ergodic MDPs and the results typically depend on $t_{mix},$ the worst-case mixing time induced by a policy. We remark that the diameter $D$ and mixing time $t_{mix}$ are both lower bounded by $sp(h^*)$, and $t_{mix}$ can be arbitrarily large for certain MDPs. On the technical side, our approach integrates two key ideas: learning an $\gamma$-discounted MDP as an approximation, and leveraging reference-advantage decomposition for variance in optimistic Q-learning. As recognized in prior work, a naive approximation by discounted MDPs results in suboptimal guarantees. A distinguishing feature of our method is maintaining estimates of value-difference between state pairs to provide a sharper bound on the variance of reference advantage. We also crucially use a careful choice of the discounted factor $\gamma$ to balance approximation error due to discounting and the statistical learning error, and we are able to maintain a good-quality reference value function with $O(SA)$ space complexity.
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Learning Neural Ranking Models Online from Implicit User Feedback
Existing online learning to rank (OL2R) solutions are limited to linear models, which are incompetent to capture possible non-linear relations between queries and documents. In this work, to unleash the power of representation learning in OL2R, we propose to directly learn a neural ranking model from users’ implicit feedback (e.g., clicks) collected on the fly. We focus on RankNet and LambdaRank, due to their great empirical success and wide adoption in offline settings, and control the notorious explore-exploit trade-off based on the convergence analysis of neural networks using neural tangent kernel. Specifically, in each round of result serving, exploration is only performed on document pairs where the predicted rank order between the two documents is uncertain; otherwise, the ranker’s predicted order will be followed in result ranking. We prove that under standard assumptions our OL2R solution achieves a gap-dependent upper regret bound of O(log 2(T)), in which the regret is defined on the total number of mis-ordered pairs over T rounds. Comparisons against an extensive set of state-of-the-art OL2R baselines on two public learning to rank benchmark datasets demonstrate the effectiveness of the proposed solution.
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- NSF-PAR ID:
- 10381227
- Date Published:
- Journal Name:
- Proceedings of the ACM Web Conference 2022
- Page Range / eLocation ID:
- 431 to 441
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3485447.3512250
