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.

Understanding the parameter estimation of softmax gating Gaussian mixture of experts has remained a long-standing open problem in the literature. It is mainly due to three fundamental theoretical challenges associated with the softmax gating function: (i) the identifiability only up to the translation of parameters; (ii) the intrinsic interaction via partial differential equations between the softmax gating and the expert functions in the Gaussian density; (iii) the complex dependence between the numerator and denominator of the conditional density of softmax gating Gaussian mixture of experts. We resolve these challenges by proposing novel Voronoi loss functions among parameters and establishing the convergence rates of maximum likelihood estimator (MLE) for solving parameter estimation in these models. When the true number of experts is unknown and over-specified, our findings show a connection between the convergence rate of the MLE and a solvability problem of a system of polynomial equations.

The Rasch model is one of the most fundamental models in \emph{item response theory} and has wide-ranging applications from education testing to recommendation systems. In a universe with $n$ users and $m$ items, the Rasch model assumes that the binary response $X_{li} \in \{0,1\}$ of a user $l$ with parameter $\theta^*_l$ to an item $i$ with parameter $\beta^*_i$ (e.g., a user likes a movie, a student correctly solves a problem) is distributed as $\Pr(X_{li}=1) = 1/(1 + \exp{-(\theta^*_l - \beta^*_i)})$. In this paper, we propose a \emph{new item estimation} algorithm for this celebrated model (i.e., to estimate $\beta^*$). The core of our algorithm is the computation of the stationary distribution of a Markov chain defined on an item-item graph. We complement our algorithmic contributions with finite-sample error guarantees, the first of their kind in the literature, showing that our algorithm is consistent and enjoys favorable optimality properties. We discuss practical modifications to accelerate and robustify the algorithm that practitioners can adopt. Experiments on synthetic and real-life datasets, ranging from small education testing datasets to large recommendation systems datasets show that our algorithm is scalable, accurate, and competitive with the most commonly used methods in the literature.

In unsupervised causal representation learning for sequential data with time-delayed latent causal influences, strong identifiability results for the disentanglement of causally-related latent variables have been established in stationary settings by leveraging temporal structure. However, in nonstationary setting, existing work only partially addressed the problem by either utilizing observed auxiliary variables (e.g., class labels and/or domain indexes) as side-information or assuming simplified latent causal dynamics. Both constrain the method to a limited range of scenarios. In this study, we further explored the Markov Assumption under time-delayed causally related process in nonstationary setting and showed that under mild conditions, the independent latent components can be recovered from their nonlinear mixture up to a permutation and a component-wise transformation, without the observation of auxiliary variables. We then introduce NCTRL, a principled estimation framework, to reconstruct time-delayed latent causal variables and identify their relations from measured sequential data only. Empirical evaluations demonstrated the reliable identification of time-delayed latent causal influences, with our methodology substantially outperforming existing baselines that fail to exploit the nonstationarity adequately and then, consequently, cannot distinguish distribution shifts.

The difficulty of identifying the physical model of complex systems has led to exploring methods that do not rely on such complex modeling of the systems. Deep reinforcement learning has been the pioneer for solving this problem without the need for relying on the physical model of complex systems by just interacting with it. However, it uses a black-box learning approach that makes it difficult to be applied within real-world and safety-critical systems without providing explanations of the actions derived by the model. Furthermore, an open research question in deep reinforcement learning is how to focus the policy learning of critical decisions within a sparse domain. This paper proposes a novel approach for the use of deep reinforcement learning in safety-critical systems. It combines the advantages of probabilistic modeling and reinforcement learning with the added benefits of interpretability and works in collaboration and synchronization with conventional decision-making strategies. The BC-SRLA is activated in specific situations which are identified autonomously through the fused information of probabilistic model and reinforcement learning, such as abnormal conditions or when the system is near-to-failure. Further, it is initialized with a baseline policy using policy cloning to allow minimum interactions with the environment to address the challenges associated with using RL in safety-critical industries. The effectiveness of the BC-SRLA is demonstrated through a case study in maintenance applied to turbofan engines, where it shows superior performance to the prior art and other baselines.

We propose weakly coupled deep Q-networks (WCDQN), a novel deep reinforcement learning algorithm that enhances performance in a class of structured problems called weakly coupled Markov decision processes (WCMDP). WCMDPs consist of multiple independent subproblems connected by an action space constraint, which is a structural property that frequently emerges in practice. Despite this appealing structure, WCMDPs quickly become intractable as the number of subproblems grows. WCDQN employs a single network to train multiple DQN "subagents", one for each subproblem, and then combine their solutions to establish an upper bound on the optimal action value. This guides the main DQN agent towards optimality. We show that the tabular version, weakly coupled Q-learning (WCQL), converges almost surely to the optimal action value. Numerical experiments show faster convergence compared to DQN and related techniques in settings with as many as 10 subproblems, $3^{10}$ total actions, and a continuous state space.

Adversarial attacks can mislead neural network classifiers. The defense against adversarial attacks is important for AI safety. Adversarial purification is a family of approaches that defend adversarial attacks with suitable pre-processing. Diffusion models have been shown to be effective for adversarial purification. Despite their success, many aspects of diffusion purification still remain unexplored. In this paper, we investigate and improve upon three limiting designs of diffusion purification: the use of an improved diffusion model, advanced numerical simulation techniques, and optimal control of randomness. Based on our findings, we propose Purify++, a new diffusion purification algorithm that is now the state-of-the-art purification method against several adversarial attacks. Our work presents a systematic exploration of the limits of diffusion purification methods.

This paper focuses on the data-insufficiency problem in multi-task learning within an episodic training setup. Specifically, we explore the potential of heterogeneous information across tasks and meta-knowledge among episodes to effectively tackle each task with limited data. Existing meta-learning methods often fail to take advantage of crucial heterogeneous information in a single episode, while multi-task learning models neglect reusing experience from earlier episodes. To address the problem of insufficient data, we develop Heterogeneous Neural Processes (HNPs) for the episodic multi-task setup. Within the framework of hierarchical Bayes, HNPs effectively capitalize on prior experiences as meta-knowledge and capture task-relatedness among heterogeneous tasks, mitigating data-insufficiency. Meanwhile, transformer-structured inference modules are designed to enable efficient inferences toward meta-knowledge and task-relatedness. In this way, HNPs can learn more powerful functional priors for adapting to novel heterogeneous tasks in each meta-test episode. Experimental results show the superior performance of the proposed HNPs over typical baselines, and ablation studies verify the effectiveness of the designed inference modules.

We present a new method of training energy-based models (EBMs) for anomaly detection that leverages low-dimensional structures within data. The proposed algorithm, Manifold Projection-Diffusion Recovery (MPDR), first perturbs a data point along a low-dimensional manifold that approximates the training dataset. Then, EBM is trained to maximize the probability of recovering the original data. The training involves the generation of negative samples via MCMC, as in conventional EBM training, but from a different distribution concentrated near the manifold. The resulting near-manifold negative samples are highly informative, reflecting relevant modes of variation in data. An energy function of MPDR effectively learns accurate boundaries of the training data distribution and excels at detecting out-of-distribution samples. Experimental results show that MPDR exhibits strong performance across various anomaly detection tasks involving diverse data types, such as images, vectors, and acoustic signals.

Deep neural networks (DNNs) are vulnerable to adversarial attacks. It is found empirically that adversarially robust generalization is crucial in establishing defense algorithms against adversarial attacks. Therefore, it is interesting to study the theoretical guarantee of robust generalization. This paper focuses on norm-based complexity, based on a PAC-Bayes approach (Neyshabur et al., 2017). The main challenge lies in extending the key ingredient, which is a weight perturbation bound in standard settings, to the robust settings. Existing attempts heavily rely on additional strong assumptions, leading to loose bounds. In this paper, we address this issue and provide a spectrally-normalized robust generalization bound for DNNs. Compared to existing bounds, our bound offers two significant advantages: Firstly, it does not depend on additional assumptions. Secondly, it is considerably tighter, aligning with the bounds of standard generalization. Therefore, our result provides a different perspective on understanding robust generalization: The mismatch terms between standard and robust generalization bounds shown in previous studies do not contribute to the poor robust generalization. Instead, these disparities solely due to mathematical issues. Finally, we extend the main result to adversarial robustness against general non-$\ell_p$ attacks and other neural network architectures.