Jian Li

Guojun Xiong, Jian Li

Multi-player multi-armed bandit is an increasingly relevant decision-making problem, motivated by applications to cognitive radio systems. Most research for this problem focuses exclusively on the settings that players have \textit{full access} to all arms and receive no reward when pulling the same arm. Hence all players solve the same bandit problem with the goal of maximizing their cumulative reward. However, these settings neglect several important factors in many real-world applications, where players have \textit{limited access} to \textit{a dynamic local subset of arms} (i.e., an arm could sometimes be ``walking'' and not accessible to the player). To this end, this paper proposes a \textit{multi-player multi-armed walking bandits} model, aiming to address aforementioned modeling issues. The goal now is to maximize the reward, however, players can only pull arms from the local subset and only collect a full reward if no other players pull the same arm. We adopt Upper Confidence Bound (UCB) to deal with the exploration-exploitation tradeoff and employ distributed optimization techniques to properly handle collisions. By carefully integrating these two techniques, we propose a decentralized algorithm with near-optimal guarantee on the regret, and can be easily implemented to obtain competitive empirical performance.

Guojun Xiong, Jian Li

Whittle index policy is a heuristic to the intractable restless multi-armed bandits (RMAB) problem. Although it is provably asymptotically optimal, finding Whittle indices remains difficult. In this paper, we present Neural-Q-Whittle, a Whittle index based Q-learning algorithm for RMAB with neural network function approximation, which is an example of nonlinear two-timescale stochastic approximation with Q-function values updated on a faster timescale and Whittle indices on a slower timescale. Despite the empirical success of deep Q-learning, the non-asymptotic convergence rate of Neural-Q-Whittle, which couples neural networks with two-timescale Q-learning largely remains unclear. This paper provides a finite-time analysis of Neural-Q-Whittle, where data are generated from a Markov chain, and Q-function is approximated by a ReLU neural network. Our analysis leverages a Lyapunov drift approach to capture the evolution of two coupled parameters, and the nonlinearity in value function approximation further requires us to characterize the approximation error. Combing these provide Neural-Q-Whittle with $\mathcal{O}(1/k^{2/3})$ convergence rate, where $k$ is the number of iterations.

Yilin Kang, Yong Liu, Jian Li et al.

In this paper, by introducing Generalized Bernstein condition, we propose the first $\mathcal{O}\big(\frac{\sqrt{p}}{nε}\big)$ high probability excess population risk bound for differentially private algorithms under the assumptions $G$-Lipschitz, $L$-smooth, and Polyak-Łojasiewicz condition, based on gradient perturbation method. If we replace the properties $G$-Lipschitz and $L$-smooth by $α$-H{ö}lder smoothness (which can be used in non-smooth setting), the high probability bound comes to $\mathcal{O}\big(n^{-\fracα{1+2α}}\big)$ w.r.t $n$, which cannot achieve $\mathcal{O}\left(1/n\right)$ when $α\in(0,1]$. To solve this problem, we propose a variant of gradient perturbation method, \textbf{max$\{1,g\}$-Normalized Gradient Perturbation} (m-NGP). We further show that by normalization, the high probability excess population risk bound under assumptions $α$-H{ö}lder smooth and Polyak-Łojasiewicz condition can achieve $\mathcal{O}\big(\frac{\sqrt{p}}{nε}\big)$, which is the first $\mathcal{O}\left(1/n\right)$ high probability excess population risk bound w.r.t $n$ for differentially private algorithms under non-smooth conditions. Moreover, we evaluate the performance of the new proposed algorithm m-NGP, the experimental results show that m-NGP improves the performance of the differentially private model over real datasets. It demonstrates that m-NGP improves the utility bound and the accuracy of the DP model on real datasets simultaneously.

Shuo Sun, Wanqi Xue, Rundong Wang et al.

Reinforcement learning (RL) techniques have shown great success in many challenging quantitative trading tasks, such as portfolio management and algorithmic trading. Especially, intraday trading is one of the most profitable and risky tasks because of the intraday behaviors of the financial market that reflect billions of rapidly fluctuating capitals. However, a vast majority of existing RL methods focus on the relatively low frequency trading scenarios (e.g., day-level) and fail to capture the fleeting intraday investment opportunities due to two major challenges: 1) how to effectively train profitable RL agents for intraday investment decision-making, which involves high-dimensional fine-grained action space; 2) how to learn meaningful multi-modality market representation to understand the intraday behaviors of the financial market at tick-level. Motivated by the efficient workflow of professional human intraday traders, we propose DeepScalper, a deep reinforcement learning framework for intraday trading to tackle the above challenges. Specifically, DeepScalper includes four components: 1) a dueling Q-network with action branching to deal with the large action space of intraday trading for efficient RL optimization; 2) a novel reward function with a hindsight bonus to encourage RL agents making trading decisions with a long-term horizon of the entire trading day; 3) an encoder-decoder architecture to learn multi-modality temporal market embedding, which incorporates both macro-level and micro-level market information; 4) a risk-aware auxiliary task to maintain a striking balance between maximizing profit and minimizing risk. Through extensive experiments on real-world market data spanning over three years on six financial futures, we demonstrate that DeepScalper significantly outperforms many state-of-the-art baselines in terms of four financial criteria.

Liang Zeng, Lei Wang, Hui Niu et al.

Price movement forecasting, aimed at predicting financial asset trends based on current market information, has achieved promising advancements through machine learning (ML) methods. Most existing ML methods, however, struggle with the extremely low signal-to-noise ratio and stochastic nature of financial data, often mistaking noises for real trading signals without careful selection of potentially profitable samples. To address this issue, we propose LARA, a novel price movement forecasting framework with two main components: Locality-Aware Attention (LA-Attention) and Iterative Refinement Labeling (RA-Labeling). (1) LA-Attention, enhanced by metric learning techniques, automatically extracts the potentially profitable samples through masked attention scheme and task-specific distance metrics. (2) RA-Labeling further iteratively refines the noisy labels of potentially profitable samples, and combines the learned predictors robust to the unseen and noisy samples. In a set of experiments on three real-world financial markets: stocks, cryptocurrencies, and ETFs, LARA significantly outperforms several machine learning based methods on the Qlib quantitative investment platform. Extensive ablation studies confirm LARA's superior ability in capturing more reliable trading opportunities.

Haotian Jiang, Jian Li, Mingda Qiao

In the Best-$K$ identification problem (Best-$K$-Arm), we are given $N$ stochastic bandit arms with unknown reward distributions. Our goal is to identify the $K$ arms with the largest means with high confidence, by drawing samples from the arms adaptively. This problem is motivated by various practical applications and has attracted considerable attention in the past decade. In this paper, we propose new practical algorithms for the Best-$K$-Arm problem, which have nearly optimal sample complexity bounds (matching the lower bound up to logarithmic factors) and outperform the state-of-the-art algorithms for the Best-$K$-Arm problem (even for $K=1$) in practice.

Wei Chen, Wei Hu, Fu Li et al.

In this paper, we study the stochastic combinatorial multi-armed bandit (CMAB) framework that allows a general nonlinear reward function, whose expected value may not depend only on the means of the input random variables but possibly on the entire distributions of these variables. Our framework enables a much larger class of reward functions such as the $\max()$ function and nonlinear utility functions. Existing techniques relying on accurate estimations of the means of random variables, such as the upper confidence bound (UCB) technique, do not work directly on these functions. We propose a new algorithm called stochastically dominant confidence bound (SDCB), which estimates the distributions of underlying random variables and their stochastically dominant confidence bounds. We prove that SDCB can achieve $O(\log{T})$ distribution-dependent regret and $\tilde{O}(\sqrt{T})$ distribution-independent regret, where $T$ is the time horizon. We apply our results to the $K$-MAX problem and expected utility maximization problems. In particular, for $K$-MAX, we provide the first polynomial-time approximation scheme (PTAS) for its offline problem, and give the first $\tilde{O}(\sqrt T)$ bound on the $(1-ε)$-approximation regret of its online problem, for any $ε>0$.