Zhiming Huang

Zhiming Huang, Bingshan Hu, Jianping Pan

We revisit combinatorial Thompson sampling (CTS) for semi-bandits with sleeping arms, where arm availability varies over time and actions must satisfy combinatorial constraints, as in wireless mesh routing with fluctuating link availability. Despite its practical relevance, CTS has been hindered by several long-standing problems: (i) the absence of worst-case regret guarantees in the semi-bandit setting even without sleeping arms, (ii) the lack of theory under adversarially varying availability, and (iii) the consistently weak empirical performance of CTS with Gaussian priors (CTS-G). This paper resolves these long-standing issues by providing the first worst-case regret analysis of CTS-G, proving an upper bound of $\tilde{O}(m\sqrt{NT})$ and a matching lower bound of $\tildeΩ(m\sqrt{NT})$. To bridge the gap between theory and practice, we further propose CL-SG, a simple CTS-G variant that samples a single shared Gaussian seed each round to coordinate exploration across arms. We show that CL-SG achieves an improved regret bound of $\tilde{O}(\sqrt{mNT})$, together with a matching lower bound $Ω(\sqrt{mNT})$. Experiments on real-world datasets demonstrate that CL-SG consistently outperforms strong baselines including CTS-G and CTS-B, and we open-source our implementation for reproducibility.

Zhiming Huang, Jamie Morgenstern, Aaron Roth et al.

We study online multicalibration beyond the worst-case. We give a single, efficient algorithm which dynamically interpolates between benign and worst-case sequences by adaptively refining a dyadic grid of prediction values. Its error is controlled by the number of leaves in the refinement tree. Our analysis recovers the known $\widetilde O(T^{2/3})$ worst-case-optimal rate for online multicalibration, while simultaneously automatically adapting to easier instances: in the marginal stochastic setting it obtains a rate of $\widetilde O(\sqrt T)$, and for piecewise-stationary means with $J$ segments its rate is $\widetilde O(\sqrt{JT})$. More generally, the rate depends on a threshold-complexity measure of the predictable mean process relative to the group family. We show that this dependence is tight up to logarithmic factors.

Bingshan Hu, Zhiming Huang, Tianyue H. Zhang et al. · mila

We address differentially private stochastic bandit problems from the angles of exploring the deep connections among Thompson Sampling with Gaussian priors, Gaussian mechanisms, and Gaussian differential privacy (GDP). We propose DP-TS-UCB, a novel parametrized private bandit algorithm that enables to trade off privacy and regret. DP-TS-UCB satisfies $ \tilde{O} \left(T^{0.25(1-α)}\right)$-GDP and enjoys an $O \left(K\ln^{α+1}(T)/Δ\right)$ regret bound, where $α\in [0,1]$ controls the trade-off between privacy and regret. Theoretically, our DP-TS-UCB relies on anti-concentration bounds of Gaussian distributions and links exploration mechanisms in Thompson Sampling-based algorithms and Upper Confidence Bound-based algorithms, which may be of independent interest.

Bingshan Hu, Zhiming Huang, Tianyue H. Zhang et al. · mila

We study Thompson Sampling-based algorithms for stochastic bandits with bounded rewards. As the existing problem-dependent regret bound for Thompson Sampling with Gaussian priors [Agrawal and Goyal, 2017] is vacuous when $T \le 288 e^{64}$, we derive a more practical bound that tightens the coefficient of the leading term %from $288 e^{64}$ to $1270$. Additionally, motivated by large-scale real-world applications that require scalability, adaptive computational resource allocation, and a balance in utility and computation, we propose two parameterized Thompson Sampling-based algorithms: Thompson Sampling with Model Aggregation (TS-MA-$α$) and Thompson Sampling with Timestamp Duelling (TS-TD-$α$), where $α\in [0,1]$ controls the trade-off between utility and computation. Both algorithms achieve $O \left(K\ln^{α+1}(T)/Δ\right)$ regret bound, where $K$ is the number of arms, $T$ is the finite learning horizon, and $Δ$ denotes the single round performance loss when pulling a sub-optimal arm.

Bingshan Hu, Zhiming Huang, Nishant A. Mehta et al.

In this paper, we study differentially private online learning problems in a stochastic environment under both bandit and full information feedback. For differentially private stochastic bandits, we propose both UCB and Thompson Sampling-based algorithms that are anytime and achieve the optimal $O \left(\sum_{j: Δ_j>0} \frac{\ln(T)}{\min \left\{Δ_j, ε\right\}} \right)$ instance-dependent regret bound, where $T$ is the finite learning horizon, $Δ_j$ denotes the suboptimality gap between the optimal arm and a suboptimal arm $j$, and $ε$ is the required privacy parameter. For the differentially private full information setting with stochastic rewards, we show an $Ω\left(\frac{\ln(K)}{\min \left\{Δ_{\min}, ε\right\}} \right)$ instance-dependent regret lower bound and an $Ω\left(\sqrt{T\ln(K)} + \frac{\ln(K)}ε\right)$ minimax lower bound, where $K$ is the total number of actions and $Δ_{\min}$ denotes the minimum suboptimality gap among all the suboptimal actions. For the same differentially private full information setting, we also present an $ε$-differentially private algorithm whose instance-dependent regret and worst-case regret match our respective lower bounds up to an extra $\log(T)$ factor.

Zhiming Huang, Yifan Xu, Bingshan Hu et al.

We study the combinatorial sleeping multi-armed semi-bandit problem with long-term fairness constraints~(CSMAB-F). To address the problem, we adopt Thompson Sampling~(TS) to maximize the total rewards and use virtual queue techniques to handle the fairness constraints, and design an algorithm called \emph{TS with beta priors and Bernoulli likelihoods for CSMAB-F~(TSCSF-B)}. Further, we prove TSCSF-B can satisfy the fairness constraints, and the time-averaged regret is upper bounded by $\frac{N}{2η} + O\left(\frac{\sqrt{mNT\ln T}}{T}\right)$, where $N$ is the total number of arms, $m$ is the maximum number of arms that can be pulled simultaneously in each round~(the cardinality constraint) and $η$ is the parameter trading off fairness for rewards. By relaxing the fairness constraints (i.e., let $η\rightarrow \infty$), the bound boils down to the first problem-independent bound of TS algorithms for combinatorial sleeping multi-armed semi-bandit problems. Finally, we perform numerical experiments and use a high-rating movie recommendation application to show the effectiveness and efficiency of the proposed algorithm.

Zhiming Huang, Lin Yang, Wen Jiang

Social dilemmas have been regarded as the essence of evolution game theory, in which the prisoner's dilemma game is the most famous metaphor for the problem of cooperation. Recent findings revealed people's behavior violated the Sure Thing Principle in such games. Classic probability methodologies have difficulty explaining the underlying mechanisms of people's behavior. In this paper, a novel quantum-like Bayesian Network was proposed to accommodate the paradoxical phenomenon. The special network can take interference into consideration, which is likely to be an efficient way to describe the underlying mechanism. With the assistance of belief entropy, named as Deng entropy, the paper proposes Belief Distance to render the model practical. Tested with empirical data, the proposed model is proved to be predictable and effective.