arXiv subjects

Zhengjia Zhuo

Publications and source records attributed to Zhengjia Zhuo.

4 recordsLinked to original sources

arXiv2026

Near-Optimal Regret for Semi-Bandit Learning of Monotone Stochastic Problems

We consider the task of learning an (approximately) optimal policy for stochastic optimization problems where the true distributions are unknown. In each period, the algorithm plays a policy for the stochastic problem and observes semi-bandit feedback, i.e., it only receives new samples from the random variables that were selected by the policy. We obtain an algorithm that works for a large class of ``monotone'' stochastic problems, including prophet inequality, Pandora's box, series testing, stochastic knapsack and stochastic matching. We obtain $\tilde{O}(\sqrt{nkT})$ regret for ``weakly'' monotone problems and $\tilde{O}(\sqrt{nT})$ regret for ``strongly'' monotone problems, where $T$ is the number of periods, $n$ is the problem dimension (number of random variables) and $k$ is the maximum support size of any random variable. This improves over previous regret bounds by a $\sqrt{n}$ factor. In fact, our dependence on $n$ and $T$ is the best-possible due the $Ω(\sqrt{nT})$ lower bound for multi-armed-bandits. Our main technique is the use of Hellinger distance in bounding the ``error'' between the true and learned distributions, and the use of a constant-factor chain rule for the Hellinger distance of dependent random variables.

cs.LG↗

arXiv2026

Semi-Bandit Learning for Monotone Stochastic Optimization

Stochastic optimization is a widely used approach for optimization under uncertainty, where uncertain input parameters are modeled by random variables. Exact or approximation algorithms have been obtained for several fundamental problems in this area. However, a significant limitation of this approach is that it requires full knowledge of the underlying probability distributions. Can we still get good (approximation) algorithms if these distributions are unknown, and the algorithm needs to learn them through repeated interactions? In this paper, we resolve this question for a large class of ''monotone'' stochastic problems, by providing a generic online learning algorithm with $\sqrt{T\log(T)}$ regret relative to the best approximation algorithm (under known distributions). Importantly, our online algorithm works in a semi-bandit setting, where in each period, the algorithm only observes samples from the random variables that were actually probed. Moreover, our result extends to settings with censored and binary feedback, where the policy only observes truncated or thresholded versions of the probed variables. Our framework applies to several fundamental problems such as prophet inequality, Pandora's box, stochastic knapsack, single-resource revenue management and sequential posted pricing.

cs.LG↗

arXiv2026

Learning Markov Decision Processes under Fully Bandit Feedback

A standard assumption in Reinforcement Learning is that the agent observes every visited state-action pair in the associated Markov Decision Process (MDP), along with the per-step rewards. Strong theoretical results are known in this setting, achieving nearly-tight $Θ(\sqrt{T})$-regret bounds. However, such detailed feedback can be unrealistic, and recent research has investigated more restricted settings such as trajectory feedback, where the agent observes all the visited state-action pairs, but only a single \emph{aggregate} reward. In this paper, we consider a far more restrictive ``fully bandit'' feedback model for episodic MDPs, where the agent does not even observe the visited state-action pairs -- it only learns the aggregate reward. We provide the first efficient bandit learning algorithm for episodic MDPs with $\widetilde{O}(\sqrt{T})$ regret. Our regret has an exponential dependence on the horizon length $\H$, which we show is necessary. We also obtain improved nearly-tight regret bounds for ``ordered'' MDPs; these can be used to model classical stochastic optimization problems such as $k$-item prophet inequality and sequential posted pricing. Finally, we evaluate the empirical performance of our algorithm for the setting of $k$-item prophet inequalities; despite the highly restricted feedback, our algorithm's performance is comparable to that of a state-of-art learning algorithm (UCB-VI) with detailed state-action feedback.

cs.LG↗

arXiv2025

A Simple Approximation Algorithm for Optimal Decision Tree

Optimal decision tree (\odt) is a fundamental problem arising in applications such as active learning, entity identification, and medical diagnosis. An instance of \odt is given by $m$ hypotheses, out of which an unknown ``true'' hypothesis is drawn according to some probability distribution. An algorithm needs to identify the true hypothesis by making queries: each query incurs a cost and has a known response for each hypothesis. The goal is to minimize the expected query cost to identify the true hypothesis. We consider the most general setting with arbitrary costs, probabilities and responses. \odt is NP-hard to approximate better than $\ln m$ and there are $O(\ln m)$ approximation algorithms known for it. However, these algorithms and/or their analyses are quite complex. Moreover, the leading constant factors are large. We provide a simple algorithm and analysis for \odt, proving an approximation ratio of $8 \ln m$.

cs.DS↗