Baoxiang Wang

Jiawei Xu, Rui Yang, Shuang Qiu et al. · tencent-ai, tsinghua

Learning policy from offline datasets through offline reinforcement learning (RL) holds promise for scaling data-driven decision-making while avoiding unsafe and costly online interactions. However, real-world data collected from sensors or humans often contains noise and errors, posing a significant challenge for existing offline RL methods, particularly when the real-world data is limited. Our study reveals that prior research focusing on adapting predominant offline RL methods based on temporal difference learning still falls short under data corruption when the dataset is limited. In contrast, we discover that vanilla sequence modeling methods, such as Decision Transformer, exhibit robustness against data corruption, even without specialized modifications. To unlock the full potential of sequence modeling, we propose Robust Decision Rransformer (RDT) by incorporating three simple yet effective robust techniques: embedding dropout to improve the model's robustness against erroneous inputs, Gaussian weighted learning to mitigate the effects of corrupted labels, and iterative data correction to eliminate corrupted data from the source. Extensive experiments on MuJoCo, Kitchen, and Adroit tasks demonstrate RDT's superior performance under various data corruption scenarios compared to prior methods. Furthermore, RDT exhibits remarkable robustness in a more challenging setting that combines training-time data corruption with test-time observation perturbations. These results highlight the potential of sequence modeling for learning from noisy or corrupted offline datasets, thereby promoting the reliable application of offline RL in real-world scenarios. Our code is available at https://github.com/jiawei415/RobustDecisionTransformer.

Jing Dong, Jingyu Wu, Siwei Wang et al.

The congestion game is a powerful model that encompasses a range of engineering systems such as traffic networks and resource allocation. It describes the behavior of a group of agents who share a common set of $F$ facilities and take actions as subsets with $k$ facilities. In this work, we study the online formulation of congestion games, where agents participate in the game repeatedly and observe feedback with randomness. We propose CongestEXP, a decentralized algorithm that applies the classic exponential weights method. By maintaining weights on the facility level, the regret bound of CongestEXP avoids the exponential dependence on the size of possible facility sets, i.e., $\binom{F}{k} \approx F^k$, and scales only linearly with $F$. Specifically, we show that CongestEXP attains a regret upper bound of $O(kF\sqrt{T})$ for every individual player, where $T$ is the time horizon. On the other hand, exploiting the exponential growth of weights enables CongestEXP to achieve a fast convergence rate. If a strict Nash equilibrium exists, we show that CongestEXP can converge to the strict Nash policy almost exponentially fast in $O(F\exp(-t^{1-α}))$, where $t$ is the number of iterations and $α\in (1/2, 1)$.

Wenhao Li, Baoxiang Wang, Shanchao Yang et al.

Enhancing the diversity of policies is beneficial for robustness, exploration, and transfer in reinforcement learning (RL). In this paper, we aim to seek diverse policies in an under-explored setting, namely RL tasks with structured action spaces with the two properties of composability and local dependencies. The complex action structure, non-uniform reward landscape, and subtle hyperparameter tuning due to the properties of structured actions prevent existing approaches from scaling well. We propose a simple and effective RL method, Diverse Policy Optimization (DPO), to model the policies in structured action space as the energy-based models (EBM) by following the probabilistic RL framework. A recently proposed novel and powerful generative model, GFlowNet, is introduced as the efficient, diverse EBM-based policy sampler. DPO follows a joint optimization framework: the outer layer uses the diverse policies sampled by the GFlowNet to update the EBM-based policies, which supports the GFlowNet training in the inner layer. Experiments on ATSC and Battle benchmarks demonstrate that DPO can efficiently discover surprisingly diverse policies in challenging scenarios and substantially outperform existing state-of-the-art methods.

Jing Dong, Shiji Zhou, Baoxiang Wang et al.

The phenomenon of data distribution evolving over time has been observed in a range of applications, calling the needs of adaptive learning algorithms. We thus study the problem of supervised gradual domain adaptation, where labeled data from shifting distributions are available to the learner along the trajectory, and we aim to learn a classifier on a target data distribution of interest. Under this setting, we provide the first generalization upper bound on the learning error under mild assumptions. Our results are algorithm agnostic, general for a range of loss functions, and only depend linearly on the averaged learning error across the trajectory. This shows significant improvement compared to the previous upper bound for unsupervised gradual domain adaptation, where the learning error on the target domain depends exponentially on the initial error on the source domain. Compared with the offline setting of learning from multiple domains, our results also suggest the potential benefits of the temporal structure among different domains in adapting to the target one. Empirically, our theoretical results imply that learning proper representations across the domains will effectively mitigate the learning errors. Motivated by these theoretical insights, we propose a min-max learning objective to learn the representation and classifier simultaneously. Experimental results on both semi-synthetic and large-scale real datasets corroborate our findings and demonstrate the effectiveness of our objectives.

Jing Dong, Jingwei Li, Baoxiang Wang et al.

Reinforcement learning (RL) has exceeded human performance in many synthetic settings such as video games and Go. However, real-world deployment of end-to-end RL models is less common, as RL models can be very sensitive to slight perturbation of the environment. The robust Markov decision process (MDP) framework -- in which the transition probabilities belong to an uncertainty set around a nominal model -- provides one way to develop robust models. While previous analysis shows RL algorithms are effective assuming access to a generative model, it remains unclear whether RL can be efficient under a more realistic online setting, which requires a careful balance between exploration and exploitation. In this work, we consider online robust MDP by interacting with an unknown nominal system. We propose a robust optimistic policy optimization algorithm that is provably efficient. To address the additional uncertainty caused by an adversarial environment, our model features a new optimistic update rule derived via Fenchel conjugates. Our analysis establishes the first regret bound for online robust MDPs.

Fang Kong, Xiangcheng Zhang, Baoxiang Wang et al.

Learning Markov decision processes (MDP) in an adversarial environment has been a challenging problem. The problem becomes even more challenging with function approximation, since the underlying structure of the loss function and transition kernel are especially hard to estimate in a varying environment. In fact, the state-of-the-art results for linear adversarial MDP achieve a regret of $\tilde{O}(K^{6/7})$ ($K$ denotes the number of episodes), which admits a large room for improvement. In this paper, we investigate the problem with a new view, which reduces linear MDP into linear optimization by subtly setting the feature maps of the bandit arms of linear optimization. This new technique, under an exploratory assumption, yields an improved bound of $\tilde{O}(K^{4/5})$ for linear adversarial MDP without access to a transition simulator. The new view could be of independent interest for solving other MDP problems that possess a linear structure.

Qi Tian, Kun Kuang, Furui Liu et al.

Offline multi-agent reinforcement learning (MARL) aims to learn effective multi-agent policies from pre-collected datasets, which is an important step toward the deployment of multi-agent systems in real-world applications. However, in practice, each individual behavior policy that generates multi-agent joint trajectories usually has a different level of how well it performs. e.g., an agent is a random policy while other agents are medium policies. In the cooperative game with global reward, one agent learned by existing offline MARL often inherits this random policy, jeopardizing the performance of the entire team. In this paper, we investigate offline MARL with explicit consideration on the diversity of agent-wise trajectories and propose a novel framework called Shared Individual Trajectories (SIT) to address this problem. Specifically, an attention-based reward decomposition network assigns the credit to each agent through a differentiable key-value memory mechanism in an offline manner. These decomposed credits are then used to reconstruct the joint offline datasets into prioritized experience replay with individual trajectories, thereafter agents can share their good trajectories and conservatively train their policies with a graph attention network (GAT) based critic. We evaluate our method in both discrete control (i.e., StarCraft II and multi-agent particle environment) and continuous control (i.e, multi-agent mujoco). The results indicate that our method achieves significantly better results in complex and mixed offline multi-agent datasets, especially when the difference of data quality between individual trajectories is large.

Canzhe Zhao, Yanjie Ze, Jing Dong et al.

Communication lays the foundation for cooperation in human society and in multi-agent reinforcement learning (MARL). Humans also desire to maintain their privacy when communicating with others, yet such privacy concern has not been considered in existing works in MARL. To this end, we propose the \textit{differentially private multi-agent communication} (DPMAC) algorithm, which protects the sensitive information of individual agents by equipping each agent with a local message sender with rigorous $(ε, δ)$-differential privacy (DP) guarantee. In contrast to directly perturbing the messages with predefined DP noise as commonly done in privacy-preserving scenarios, we adopt a stochastic message sender for each agent respectively and incorporate the DP requirement into the sender, which automatically adjusts the learned message distribution to alleviate the instability caused by DP noise. Further, we prove the existence of a Nash equilibrium in cooperative MARL with privacy-preserving communication, which suggests that this problem is game-theoretically learnable. Extensive experiments demonstrate a clear advantage of DPMAC over baseline methods in privacy-preserving scenarios.

Yue Lin, Wenhao Li, Hongyuan Zha et al.

Reinforcement learning (RL) is inspired by the way human infants and animals learn from the environment. The setting is somewhat idealized because, in actual tasks, other agents in the environment have their own goals and behave adaptively to the ego agent. To thrive in those environments, the agent needs to influence other agents so their actions become more helpful and less harmful. Research in computational economics distills two ways to influence others directly: by providing tangible goods (mechanism design) and by providing information (information design). This work investigates information design problems for a group of RL agents. The main challenges are two-fold. One is the information provided will immediately affect the transition of the agent trajectories, which introduces additional non-stationarity. The other is the information can be ignored, so the sender must provide information that the receiver is willing to respect. We formulate the Markov signaling game, and develop the notions of signaling gradient and the extended obedience constraints that address these challenges. Our algorithm is efficient on various mixed-motive tasks and provides further insights into computational economics. Our code is publicly available at https://github.com/YueLin301/InformationDesignMARL.

Yingru Li, Jiawei Xu, Baoxiang Wang et al.

Thompson Sampling is a principled method for balancing exploration and exploitation, but its real-world adoption faces computational challenges in large-scale or non-conjugate settings. While ensemble-based approaches offer partial remedies, they typically require prohibitively large ensemble sizes. We propose Ensemble++, a scalable exploration framework using a novel shared-factor ensemble architecture with random linear combinations. For linear bandits, we provide theoretical guarantees showing that Ensemble++ achieves regret comparable to exact Thompson Sampling with only $Θ(d \log T)$ ensemble sizes--significantly outperforming prior methods. Crucially, this efficiency holds across both compact and finite action sets with either time-invariant or time-varying contexts without configuration changes. We extend this theoretical foundation to nonlinear rewards by replacing fixed features with learnable neural representations while preserving the same incremental update principle, effectively bridging theory and practice for real-world tasks. Comprehensive experiments across linear, quadratic, neural, and GPT-based contextual bandits validate our theoretical findings and demonstrate Ensemble++'s superior regret-computation tradeoff versus state-of-the-art methods.

Jing Dong, Baoxiang Wang, Yaoliang Yu

In this work, we study potential games and Markov potential games under stochastic cost and bandit feedback. We propose a variant of the Frank-Wolfe algorithm with sufficient exploration and recursive gradient estimation, which provably converges to the Nash equilibrium while attaining sublinear regret for each individual player. Our algorithm simultaneously achieves a Nash regret and a regret bound of $O(T^{4/5})$ for potential games, which matches the best available result, without using additional projection steps. Through carefully balancing the reuse of past samples and exploration of new samples, we then extend the results to Markov potential games and improve the best available Nash regret from $O(T^{5/6})$ to $O(T^{4/5})$. Moreover, our algorithm requires no knowledge of the game, such as the distribution mismatch coefficient, which provides more flexibility in its practical implementation. Experimental results corroborate our theoretical findings and underscore the practical effectiveness of our method.

Fang Kong, Jize Xie, Baoxiang Wang et al.

We study online influence maximization (OIM) under a new model of decreasing cascade (DC). This model is a generalization of the independent cascade (IC) model by considering the common phenomenon of market saturation. In DC, the chance of an influence attempt being successful reduces with previous failures. The effect is neglected by previous OIM works under IC and linear threshold models. We propose the DC-UCB algorithm to solve this problem, which achieves a regret bound of the same order as the state-of-the-art works on the IC model. Extensive experiments on both synthetic and real datasets show the effectiveness of our algorithm.

Wenhao Li, Dan Qiao, Baoxiang Wang et al.

The difficulty of appropriately assigning credit is particularly heightened in cooperative MARL with sparse reward, due to the concurrent time and structural scales involved. Automatic subgoal generation (ASG) has recently emerged as a viable MARL approach inspired by utilizing subgoals in intrinsically motivated reinforcement learning. However, end-to-end learning of complex task planning from sparse rewards without prior knowledge, undoubtedly requires massive training samples. Moreover, the diversity-promoting nature of existing ASG methods can lead to the "over-representation" of subgoals, generating numerous spurious subgoals of limited relevance to the actual task reward and thus decreasing the sample efficiency of the algorithm. To address this problem and inspired by the disentangled representation learning, we propose a novel "disentangled" decision-making method, Semantically Aligned task decomposition in MARL (SAMA), that prompts pretrained language models with chain-of-thought that can suggest potential goals, provide suitable goal decomposition and subgoal allocation as well as self-reflection-based replanning. Additionally, SAMA incorporates language-grounded RL to train each agent's subgoal-conditioned policy. SAMA demonstrates considerable advantages in sample efficiency compared to state-of-the-art ASG methods, as evidenced by its performance on two challenging sparse-reward tasks, Overcooked and MiniRTS.

Jing Dong, Li Shen, Yinggan Xu et al.

We study the convergence of the actor-critic algorithm with nonlinear function approximation under a nonconvex-nonconcave primal-dual formulation. Stochastic gradient descent ascent is applied with an adaptive proximal term for robust learning rates. We show the first efficient convergence result with primal-dual actor-critic with a convergence rate of $\mathcal{O}\left(\sqrt{\frac{\ln \left(N d G^2 \right)}{N}}\right)$ under Markovian sampling, where $G$ is the element-wise maximum of the gradient, $N$ is the number of iterations, and $d$ is the dimension of the gradient. Our result is presented with only the Polyak-Łojasiewicz condition for the dual variables, which is easy to verify and applicable to a wide range of reinforcement learning (RL) scenarios. The algorithm and analysis are general enough to be applied to other RL settings, like multi-agent RL. Empirical results on OpenAI Gym continuous control tasks corroborate our theoretical findings.

Canzhe Zhao, Yanjie Ze, Jing Dong et al.

Temporal difference (TD) learning is a widely used method to evaluate policies in reinforcement learning. While many TD learning methods have been developed in recent years, little attention has been paid to preserving privacy and most of the existing approaches might face the concerns of data privacy from users. To enable complex representative abilities of policies, in this paper, we consider preserving privacy in TD learning with nonlinear value function approximation. This is challenging because such a nonlinear problem is usually studied in the formulation of stochastic nonconvex-strongly-concave optimization to gain finite-sample analysis, which would require simultaneously preserving the privacy on primal and dual sides. To this end, we employ a momentum-based stochastic gradient descent ascent to achieve a single-timescale algorithm, and achieve a good trade-off between meaningful privacy and utility guarantees of both the primal and dual sides by perturbing the gradients on both sides using well-calibrated Gaussian noises. As a result, our DPTD algorithm could provide $(ε,δ)$-differential privacy (DP) guarantee for the sensitive information encoded in transitions and retain the original power of TD learning, with the utility upper bounded by $\widetilde{\mathcal{O}}(\frac{(d\log(1/δ))^{1/8}}{(nε)^{1/4}})$ (The tilde in this paper hides the log factor.), where $n$ is the trajectory length and $d$ is the dimension. Extensive experiments conducted in OpenAI Gym show the advantages of our proposed algorithm.

Qi Tian, Kun Kuang, Baoxiang Wang et al.

Communication is one of the core components for cooperative multi-agent reinforcement learning (MARL). The communication bandwidth, in many real applications, is always subject to certain constraints. To improve communication efficiency, in this article, we propose to simultaneously optimize whom to communicate with and what to communicate for each agent in MARL. By initiating the communication between agents with a directed complete graph, we propose a novel communication model, named Communicative Graph Information Bottleneck Network (CGIBNet), to simultaneously compress the graph structure and the node information with the graph information bottleneck principle. The graph structure compression is designed to cut the redundant edges for determining whom to communicate with. The node information compression aims to address the problem of what to communicate via learning compact node representations. Moreover, CGIBNet is the first universal module for bandwidth-constrained communication, which can be applied to various training frameworks (i.e., policy-based and value-based MARL frameworks) and communication modes (i.e., single-round and multi-round communication). Extensive experiments are conducted in Traffic Control and StarCraft II environments. The results indicate that our method can achieve better performance in bandwidth-constrained settings compared with state-of-the-art algorithms.

Shanchao Yang, Kaili Ma, Baoxiang Wang et al.

Improving the resilience of a network is a fundamental problem in network science, which protects the underlying system from natural disasters and malicious attacks. This is traditionally achieved via successive degree-preserving edge rewiring operations, with the major limitation of being transductive. Inductively solving graph-related tasks with sequential actions is accomplished by adopting graph neural networks (GNNs) coupled with reinforcement learning under the scenario with rich graph features. However, such frameworks cannot be directly applied to resilience tasks where only pure topological structure is available. In this case, GNNs can barely learn useful information, resulting in prohibitive difficulty in making actions for successively rewiring edges under a reinforcement learning context. In this paper, we study in depth the reasons why typical GNNs cause such failure. Based on this investigation, we propose ResiNet, the first end-to-end trainable inductive framework to discover resilient network topologies while balancing network utility. To this end, we reformulate resilience optimization as an MDP equipped with edge rewiring action space, and propose a pure topology-oriented variant of GNN called filtration enhanced graph neural network (FireGNN), which can learn from graphs without rich features. Extensive experiments demonstrate that ResiNet achieves a near-optimal resilience gain on various graphs while balancing the utility, and outperforms existing approaches by a large margin.

Jing Dong, Shuai Li, Baoxiang Wang

Motivated by the common strategic activities in crowdsourcing labeling, we study the problem of sequential eliciting information without verification (EIWV) for workers with a heterogeneous and unknown crowd. We propose a reinforcement learning-based approach that is effective against a wide range of settings including potential irrationality and collusion among workers. With the aid of a costly oracle and the inference method, our approach dynamically decides the oracle calls and gains robustness even under the presence of frequent collusion activities. Extensive experiments show the advantage of our approach. Our results also present the first comprehensive experiments of EIWV on large-scale real datasets and the first thorough study of the effects of environmental variables.

Jiahui Li, Kun Kuang, Baoxiang Wang et al.

Centralized Training with Decentralized Execution (CTDE) has been a popular paradigm in cooperative Multi-Agent Reinforcement Learning (MARL) settings and is widely used in many real applications. One of the major challenges in the training process is credit assignment, which aims to deduce the contributions of each agent according to the global rewards. Existing credit assignment methods focus on either decomposing the joint value function into individual value functions or measuring the impact of local observations and actions on the global value function. These approaches lack a thorough consideration of the complicated interactions among multiple agents, leading to an unsuitable assignment of credit and subsequently mediocre results on MARL. We propose Shapley Counterfactual Credit Assignment, a novel method for explicit credit assignment which accounts for the coalition of agents. Specifically, Shapley Value and its desired properties are leveraged in deep MARL to credit any combinations of agents, which grants us the capability to estimate the individual credit for each agent. Despite this capability, the main technical difficulty lies in the computational complexity of Shapley Value who grows factorially as the number of agents. We instead utilize an approximation method via Monte Carlo sampling, which reduces the sample complexity while maintaining its effectiveness. We evaluate our method on StarCraft II benchmarks across different scenarios. Our method outperforms existing cooperative MARL algorithms significantly and achieves the state-of-the-art, with especially large margins on tasks with more severe difficulties.

Kun Wang, Jing Dong, Baoxiang Wang et al.

This paper studies \emph{differential privacy (DP)} and \emph{local differential privacy (LDP)} in cascading bandits. Under DP, we propose an algorithm which guarantees $ε$-indistinguishability and a regret of $\mathcal{O}((\frac{\log T}ε)^{1+ξ})$ for an arbitrarily small $ξ$. This is a significant improvement from the previous work of $\mathcal{O}(\frac{\log^3 T}ε)$ regret. Under ($ε$,$δ$)-LDP, we relax the $K^2$ dependence through the tradeoff between privacy budget $ε$ and error probability $δ$, and obtain a regret of $\mathcal{O}(\frac{K\log (1/δ) \log T}{ε^2})$, where $K$ is the size of the arm subset. This result holds for both Gaussian mechanism and Laplace mechanism by analyses on the composition. Our results extend to combinatorial semi-bandit. We show respective lower bounds for DP and LDP cascading bandits. Extensive experiments corroborate our theoretic findings.

Jing Dong, Ke Li, Shuai Li et al.

Strategic behavior against sequential learning methods, such as "click framing" in real recommendation systems, have been widely observed. Motivated by such behavior we study the problem of combinatorial multi-armed bandits (CMAB) under strategic manipulations of rewards, where each arm can modify the emitted reward signals for its own interest. This characterization of the adversarial behavior is a relaxation of previously well-studied settings such as adversarial attacks and adversarial corruption. We propose a strategic variant of the combinatorial UCB algorithm, which has a regret of at most $O(m\log T + m B_{max})$ under strategic manipulations, where $T$ is the time horizon, $m$ is the number of arms, and $B_{max}$ is the maximum budget of an arm. We provide lower bounds on the budget for arms to incur certain regret of the bandit algorithm. Extensive experiments on online worker selection for crowdsourcing systems, online influence maximization and online recommendations with both synthetic and real datasets corroborate our theoretical findings on robustness and regret bounds, in a variety of regimes of manipulation budgets.

Andrej Bogdanov, Baoxiang Wang

$ $Let $F$ be a multivariate function from a product set $Σ^n$ to an Abelian group $G$. A $k$-partition of $F$ with cost $δ$ is a partition of the set of variables $\mathbf{V}$ into $k$ non-empty subsets $(\mathbf{X}_1, \dots, \mathbf{X}_k)$ such that $F(\mathbf{V})$ is $δ$-close to $F_1(\mathbf{X}_1)+\dots+F_k(\mathbf{X}_k)$ for some $F_1, \dots, F_k$ with respect to a given error metric. We study algorithms for agnostically learning $k$ partitions and testing $k$-partitionability over various groups and error metrics given query access to $F$. In particular we show that $1.$ Given a function that has a $k$-partition of cost $δ$, a partition of cost $\mathcal{O}(k n^2)(δ+ ε)$ can be learned in time $\tilde{\mathcal{O}}(n^2 \mathrm{poly} (1/ε))$ for any $ε> 0$. In contrast, for $k = 2$ and $n = 3$ learning a partition of cost $δ+ ε$ is NP-hard. $2.$ When $F$ is real-valued and the error metric is the 2-norm, a 2-partition of cost $\sqrt{δ^2 + ε}$ can be learned in time $\tilde{\mathcal{O}}(n^5/ε^2)$. $3.$ When $F$ is $\mathbb{Z}_q$-valued and the error metric is Hamming weight, $k$-partitionability is testable with one-sided error and $\mathcal{O}(kn^3/ε)$ non-adaptive queries. We also show that even two-sided testers require $Ω(n)$ queries when $k = 2$. This work was motivated by reinforcement learning control tasks in which the set of control variables can be partitioned. The partitioning reduces the task into multiple lower-dimensional ones that are relatively easier to learn. Our second algorithm empirically increases the scores attained over previous heuristic partitioning methods applied in this context.

Baoxiang Wang, Shuai Li, Jiajin Li et al.

We analyze the Gambler's problem, a simple reinforcement learning problem where the gambler has the chance to double or lose the bets until the target is reached. This is an early example introduced in the reinforcement learning textbook by Sutton and Barto (2018), where they mention an interesting pattern of the optimal value function with high-frequency components and repeating non-smooth points. It is however without further investigation. We provide the exact formula for the optimal value function for both the discrete and the continuous cases. Though simple as it might seem, the value function is pathological: fractal, self-similar, derivative taking either zero or infinity, and not written as elementary functions. It is in fact one of the generalized Cantor functions, where it holds a complexity that has been uncharted thus far. Our analyses could provide insights into improving value function approximation, gradient-based algorithms, and Q-learning, in real applications and implementations.

Baoxiang Wang

Binary determination of the presence of objects is one of the problems where humans perform extraordinarily better than computer vision systems, in terms of both speed and preciseness. One of the possible reasons is that humans can skip most of the clutter and attend only on salient regions. Recurrent attention models (RAM) are the first computational models to imitate the way humans process images via the REINFORCE algorithm. Despite that RAM is originally designed for image recognition, we extend it and present recurrent existence determination, an attention-based mechanism to solve the existence determination. Our algorithm employs a novel $k$-maximum aggregation layer and a new reward mechanism to address the issue of delayed rewards, which would have caused the instability of the training process. The experimental analysis demonstrates significant efficiency and accuracy improvement over existing approaches, on both synthetic and real-world datasets.

Baoxiang Wang, Nidhi Hegde

We consider differentially private algorithms for reinforcement learning in continuous spaces, such that neighboring reward functions are indistinguishable. This protects the reward information from being exploited by methods such as inverse reinforcement learning. Existing studies that guarantee differential privacy are not extendable to infinite state spaces, as the noise level to ensure privacy will scale accordingly to infinity. Our aim is to protect the value function approximator, without regard to the number of states queried to the function. It is achieved by adding functional noise to the value function iteratively in the training. We show rigorous privacy guarantees by a series of analyses on the kernel of the noise space, the probabilistic bound of such noise samples, and the composition over the iterations. We gain insight into the utility analysis by proving the algorithm's approximate optimality when the state space is discrete. Experiments corroborate our theoretical findings and show improvement over existing approaches.

Baoxiang Wang, Tongfang Sun, Xianjun Sam Zheng

In recent years, reinforcement learning (RL) methods have been applied to model gameplay with great success, achieving super-human performance in various environments, such as Atari, Go, and Poker. However, those studies mostly focus on winning the game and have largely ignored the rich and complex human motivations, which are essential for understanding different players' diverse behaviors. In this paper, we present a novel method called Multi-Motivation Behavior Modeling (MMBM) that takes the multifaceted human motivations into consideration and models the underlying value structure of the players using inverse RL. Our approach does not require the access to the dynamic of the system, making it feasible to model complex interactive environments such as massively multiplayer online games. MMBM is tested on the World of Warcraft Avatar History dataset, which recorded over 70,000 users' gameplay spanning three years period. Our model reveals the significant difference of value structures among different player groups. Using the results of motivation modeling, we also predict and explain their diverse gameplay behaviors and provide a quantitative assessment of how the redesign of the game environment impacts players' behaviors.

Kenny Young, Baoxiang Wang, Matthew E. Taylor

Reinforcement learning (RL) has had many successes in both "deep" and "shallow" settings. In both cases, significant hyperparameter tuning is often required to achieve good performance. Furthermore, when nonlinear function approximation is used, non-stationarity in the state representation can lead to learning instability. A variety of techniques exist to combat this --- most notably large experience replay buffers or the use of multiple parallel actors. These techniques come at the cost of moving away from the online RL problem as it is traditionally formulated (i.e., a single agent learning online without maintaining a large database of training examples). Meta-learning can potentially help with both these issues by tuning hyperparameters online and allowing the algorithm to more robustly adjust to non-stationarity in a problem. This paper applies meta-gradient descent to derive a set of step-size tuning algorithms specifically for online RL control with eligibility traces. Our novel technique, Metatrace, makes use of an eligibility trace analogous to methods like $TD(λ)$. We explore tuning both a single scalar step-size and a separate step-size for each learned parameter. We evaluate Metatrace first for control with linear function approximation in the classic mountain car problem and then in a noisy, non-stationary version. Finally, we apply Metatrace for control with nonlinear function approximation in 5 games in the Arcade Learning Environment where we explore how it impacts learning speed and robustness to initial step-size choice. Results show that the meta-step-size parameter of Metatrace is easy to set, Metatrace can speed learning, and Metatrace can allow an RL algorithm to deal with non-stationarity in the learning task.

Jiajin Li, Baoxiang Wang

Policy optimization on high-dimensional continuous control tasks exhibits its difficulty caused by the large variance of the policy gradient estimators. We present the action subspace dependent gradient (ASDG) estimator which incorporates the Rao-Blackwell theorem (RB) and Control Variates (CV) into a unified framework to reduce the variance. To invoke RB, our proposed algorithm (POSA) learns the underlying factorization structure among the action space based on the second-order advantage information. POSA captures the quadratic information explicitly and efficiently by utilizing the wide & deep architecture. Empirical studies show that our proposed approach demonstrates the performance improvements on high-dimensional synthetic settings and OpenAI Gym's MuJoCo continuous control tasks.