Q-learning has become an important part of the reinforcement learning toolkit since its introduction in the dissertation of Chris Watkins in the 1980s. The purpose of this paper is in part a tutorial on stochastic approximation and Q-learning, providing details regarding the INFORMS APS inaugural Applied Probability Trust Plenary Lecture, presented in Nancy France, June 2023. The paper also presents new approaches to ensure stability and potentially accelerated convergence for these algorithms, and stochastic approximation in other settings. Two contributions are entirely new: 1. Stability of Q-learning with linear function approximation has been an open topic for research for over three decades. It is shown that with appropriate optimistic training in the form of a modified Gibbs policy, there exists a solution to the projected Bellman equation, and the algorithm is stable (in terms of bounded parameter estimates). Convergence remains one of many open topics for research. 2. The new Zap Zero algorithm is designed to approximate the Newton-Raphson flow without matrix inversion. It is stable and convergent under mild assumptions on the mean flow vector field for the algorithm, and compatible statistical assumption on an underlying Markov chain. The algorithm is a general approach to stochastic approximation which in particular applies to Q-learning with "oblivious" training even with non-linear function approximation.

Navigating safely and efficiently in dense and heterogeneous traffic scenarios is challenging for autonomous vehicles (AVs) due to their inability to infer the behaviors or intentions of nearby drivers. In this work, we introduce a distributed multi-agent reinforcement learning (MARL) algorithm that can predict trajectories and intents in dense and heterogeneous traffic scenarios. Our approach for intent-aware planning, iPLAN, allows agents to infer nearby drivers' intents solely from their local observations. We model two distinct incentives for agents' strategies: Behavioral Incentive for high-level decision-making based on their driving behavior or personality and Instant Incentive for motion planning for collision avoidance based on the current traffic state. Our approach enables agents to infer their opponents' behavior incentives and integrate this inferred information into their decision-making and motion-planning processes. We perform experiments on two simulation environments, Non-Cooperative Navigation and Heterogeneous Highway. In Heterogeneous Highway, results show that, compared with centralized training decentralized execution (CTDE) MARL baselines such as QMIX and MAPPO, our method yields a 4.3% and 38.4% higher episodic reward in mild and chaotic traffic, with 48.1% higher success rate and 80.6% longer survival time in chaotic traffic. We also compare with a decentralized training decentralized execution (DTDE) baseline IPPO and demonstrate a higher episodic reward of 12.7% and 6.3% in mild traffic and chaotic traffic, 25.3% higher success rate, and 13.7% longer survival time.

We consider Linear Stochastic Approximation (LSA) with a constant stepsize and Markovian data. Viewing the joint process of the data and LSA iterate as a time-homogeneous Markov chain, we prove its convergence to a unique limiting and stationary distribution in Wasserstein distance and establish non-asymptotic, geometric convergence rates. Furthermore, we show that the bias vector of this limit admits an infinite series expansion with respect to the stepsize. Consequently, the bias is proportional to the stepsize up to higher order terms. This result stands in contrast with LSA under i.i.d. data, for which the bias vanishes. In the reversible chain setting, we provide a general characterization of the relationship between the bias and the mixing time of the Markovian data, establishing that they are roughly proportional to each other. While Polyak-Ruppert tail-averaging reduces the variance of the LSA iterates, it does not affect the bias. The above characterization allows us to show that the bias can be reduced using Richardson-Romberg extrapolation with $m\ge 2$ stepsizes, which eliminates the $m-1$ leading terms in the bias expansion. This extrapolation scheme leads to an exponentially smaller bias and an improved mean squared error, both in theory and empirically. Our results immediately apply to the Temporal Difference learning algorithm with linear function approximation, Markovian data, and constant stepsizes.

Cooperative Multi-agent Reinforcement Learning (MARL) algorithms with Zero-Shot Coordination (ZSC) have gained significant attention in recent years. ZSC refers to the ability of agents to coordinate zero-shot (without additional interaction experience) with independently trained agents. While ZSC is crucial for cooperative MARL agents, it might not be possible for complex tasks and changing environments. Agents also need to adapt and improve their performance with minimal interaction with other agents. In this work, we show empirically that state-of-the-art ZSC algorithms have poor performance when paired with agents trained with different learning methods, and they require millions of interaction samples to adapt to these new partners. To investigate this issue, we formally defined a framework based on a popular cooperative multi-agent game called Hanabi to evaluate the adaptability of MARL methods. In particular, we created a diverse set of pre-trained agents and defined a new metric called adaptation regret that measures the agent's ability to efficiently adapt and improve its coordination performance when paired with some held-out pool of partners on top of its ZSC performance. After evaluating several SOTA algorithms using our framework, our experiments reveal that naive Independent Q-Learning (IQL) agents in most cases adapt as quickly as the SOTA ZSC algorithm Off-Belief Learning (OBL). This finding raises an interesting research question: How to design MARL algorithms with high ZSC performance and capability of fast adaptation to unseen partners. As a first step, we studied the role of different hyper-parameters and design choices on the adaptability of current MARL algorithms. Our experiments show that two categories of hyper-parameters controlling the training data diversity and optimization process have a significant impact on the adaptability of Hanabi agents.

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 $(\epsilon, \delta)$-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.

We investigate a framework for binary image denoising via restricted Boltzmann machines (RBMs) that introduces a denoising objective in quadratic unconstrained binary optimization (QUBO) form and is well-suited for quantum annealing. The denoising objective is attained by balancing the distribution learned by a trained RBM with a penalty term for derivations from the noisy image. We derive the statistically optimal choice of the penalty parameter assuming the target distribution has been well-approximated, and further suggest an empirically supported modification to make the method robust to that idealistic assumption. We also show under additional assumptions that the denoised images attained by our method are, in expectation, strictly closer to the noise-free images than the noisy images are. While we frame the model as an image denoising model, it can be applied to any binary data. As the QUBO formulation is well-suited for implementation on quantum annealers, we test the model on a D-Wave Advantage machine, and also test on data too large for current quantum annealers by approximating QUBO solutions through classical heuristics.

Multi-objective Markov decision processes are a special kind of multi-objective optimization problem that involves sequential decision making while satisfying the Markov property of stochastic processes. Multi-objective reinforcement learning methods address this problem by fusing the reinforcement learning paradigm with multi-objective optimization techniques. One major drawback of these methods is the lack of adaptability to non-stationary dynamics in the environment. This is because they adopt optimization procedures that assume stationarity to evolve a coverage set of policies that can solve the problem. This paper introduces a developmental optimization approach that can evolve the policy coverage set while exploring the preference space over the defined objectives in an online manner. We propose a novel multi-objective reinforcement learning algorithm that can robustly evolve a convex coverage set of policies in an online manner in non-stationary environments. We compare the proposed algorithm with two state-of-the-art multi-objective reinforcement learning algorithms in stationary and non-stationary environments. Results showed that the proposed algorithm significantly outperforms the existing algorithms in non-stationary environments while achieving comparable results in stationary environments.

Multi-objective Markov decision processes are sequential decision-making problems that involve multiple conflicting reward functions that cannot be optimized simultaneously without a compromise. This type of problems cannot be solved by a single optimal policy as in the conventional case. Alternatively, multi-objective reinforcement learning methods evolve a coverage set of optimal policies that can satisfy all possible preferences in solving the problem. However, many of these methods cannot generalize their coverage sets to work in non-stationary environments. In these environments, the parameters of the state transition and reward distribution vary over time. This limitation results in significant performance degradation for the evolved policy sets. In order to overcome this limitation, there is a need to learn a generic skill set that can bootstrap the evolution of the policy coverage set for each shift in the environment dynamics therefore, it can facilitate a continuous learning process. In this work, intrinsically motivated reinforcement learning has been successfully deployed to evolve generic skill sets for learning hierarchical policies to solve multi-objective Markov decision processes. We propose a novel dual-phase intrinsically motivated reinforcement learning method to address this limitation. In the first phase, a generic set of skills is learned. While in the second phase, this set is used to bootstrap policy coverage sets for each shift in the environment dynamics. We show experimentally that the proposed method significantly outperforms state-of-the-art multi-objective reinforcement methods in a dynamic robotics environment.

This paper addresses the lower limits of encoding and processing the information acquired through interactions between an internal system (robot algorithms or software) and an external system (robot body and its environment) in terms of action and observation histories. Both are modeled as transition systems. We want to know the weakest internal system that is sufficient for achieving passive (filtering) and active (planning) tasks. We introduce the notion of an information transition system for the internal system which is a transition system over a space of information states that reflect a robot's or other observer's perspective based on limited sensing, memory, computation, and actuation. An information transition system is viewed as a filter and a policy or plan is viewed as a function that labels the states of this information transition system. Regardless of whether internal systems are obtained by learning algorithms, planning algorithms, or human insight, we want to know the limits of feasibility for given robot hardware and tasks. We establish, in a general setting, that minimal information transition systems exist up to reasonable equivalence assumptions, and are unique under some general conditions. We then apply the theory to generate new insights into several problems, including optimal sensor fusion/filtering, solving basic planning tasks, and finding minimal representations for modeling a system given input-output relations.

A learner aims to minimize a function $f$ by repeatedly querying a distributed oracle that provides noisy gradient evaluations. At the same time, the learner seeks to hide $\arg\min f$ from a malicious eavesdropper that observes the learner's queries. This paper considers the problem of \textit{covert} or \textit{learner-private} optimization, where the learner has to dynamically choose between learning and obfuscation by exploiting the stochasticity. The problem of controlling the stochastic gradient algorithm for covert optimization is modeled as a Markov decision process, and we show that the dynamic programming operator has a supermodular structure implying that the optimal policy has a monotone threshold structure. A computationally efficient policy gradient algorithm is proposed to search for the optimal querying policy without knowledge of the transition probabilities. As a practical application, our methods are demonstrated on a hate speech classification task in a federated setting where an eavesdropper can use the optimal weights to generate toxic content, which is more easily misclassified. Numerical results show that when the learner uses the optimal policy, an eavesdropper can only achieve a validation accuracy of $52\%$ with no information and $69\%$ when it has a public dataset with 10\% positive samples compared to $83\%$ when the learner employs a greedy policy.