Satinder Singh

David Abel, André Barreto, Hado van Hasselt et al. · deepmind, stanford

When has an agent converged? Standard models of the reinforcement learning problem give rise to a straightforward definition of convergence: An agent converges when its behavior or performance in each environment state stops changing. However, as we shift the focus of our learning problem from the environment's state to the agent's state, the concept of an agent's convergence becomes significantly less clear. In this paper, we propose two complementary accounts of agent convergence in a framing of the reinforcement learning problem that centers around bounded agents. The first view says that a bounded agent has converged when the minimal number of states needed to describe the agent's future behavior cannot decrease. The second view says that a bounded agent has converged just when the agent's performance only changes if the agent's internal state changes. We establish basic properties of these two definitions, show that they accommodate typical views of convergence in standard settings, and prove several facts about their nature and relationship. We take these perspectives, definitions, and analysis to bring clarity to a central idea of the field.

John Holler, Risto Vuorio, Zhiwei Qin et al.

Order dispatching and driver repositioning (also known as fleet management) in the face of spatially and temporally varying supply and demand are central to a ride-sharing platform marketplace. Hand-crafting heuristic solutions that account for the dynamics in these resource allocation problems is difficult, and may be better handled by an end-to-end machine learning method. Previous works have explored machine learning methods to the problem from a high-level perspective, where the learning method is responsible for either repositioning the drivers or dispatching orders, and as a further simplification, the drivers are considered independent agents maximizing their own reward functions. In this paper we present a deep reinforcement learning approach for tackling the full fleet management and dispatching problems. In addition to treating the drivers as individual agents, we consider the problem from a system-centric perspective, where a central fleet management agent is responsible for decision-making for all drivers.

Junhyuk Oh, Yijie Guo, Satinder Singh et al.

This paper proposes Self-Imitation Learning (SIL), a simple off-policy actor-critic algorithm that learns to reproduce the agent's past good decisions. This algorithm is designed to verify our hypothesis that exploiting past good experiences can indirectly drive deep exploration. Our empirical results show that SIL significantly improves advantage actor-critic (A2C) on several hard exploration Atari games and is competitive to the state-of-the-art count-based exploration methods. We also show that SIL improves proximal policy optimization (PPO) on MuJoCo tasks.

Aditya Modi, Nan Jiang, Satinder Singh et al.

We consider a reinforcement learning (RL) setting in which the agent interacts with a sequence of episodic MDPs. At the start of each episode the agent has access to some side-information or context that determines the dynamics of the MDP for that episode. Our setting is motivated by applications in healthcare where baseline measurements of a patient at the start of a treatment episode form the context that may provide information about how the patient might respond to treatment decisions. We propose algorithms for learning in such Contextual Markov Decision Processes (CMDPs) under an assumption that the unobserved MDP parameters vary smoothly with the observed context. We also give lower and upper PAC bounds under the smoothness assumption. Because our lower bound has an exponential dependence on the dimension, we consider a tractable linear setting where the context is used to create linear combinations of a finite set of MDPs. For the linear setting, we give a PAC learning algorithm based on KWIK learning techniques.

Qi Zhang, Satinder Singh, Edmund Durfee

In cooperative multiagent planning, it can often be beneficial for an agent to make commitments about aspects of its behavior to others, allowing them in turn to plan their own behaviors without taking the agent's detailed behavior into account. Extending previous work in the Bayesian setting, we consider instead a worst-case setting in which the agent has a set of possible environments (MDPs) it could be in, and develop a commitment semantics that allows for probabilistic guarantees on the agent's behavior in any of the environments it could end up facing. Crucially, an agent receives observations (of reward and state transitions) that allow it to potentially eliminate possible environments and thus obtain higher utility by adapting its policy to the history of observations. We develop algorithms and provide theory and some preliminary empirical results showing that they ensure an agent meets its commitments with history-dependent policies while minimizing maximum regret over the possible environments.

Michael Kearns, Yishay Mansour, Satinder Singh

Stochastic games generalize Markov decision processes (MDPs) to a multiagent setting by allowing the state transitions to depend jointly on all player actions, and having rewards determined by multiplayer matrix games at each state. We consider the problem of computing Nash equilibria in stochastic games, the analogue of planning in MDPs. We begin by providing a generalization of finite-horizon value iteration that computes a Nash strategy for each player in generalsum stochastic games. The algorithm takes an arbitrary Nash selection function as input, which allows the translation of local choices between multiple Nash equilibria into the selection of a single global Nash equilibrium. Our main technical result is an algorithm for computing near-Nash equilibria in large or infinite state spaces. This algorithm builds on our finite-horizon value iteration algorithm, and adapts the sparse sampling methods of Kearns, Mansour and Ng (1999) to stochastic games. We conclude by descrbing a counterexample showing that infinite-horizon discounted value iteration, which was shown by shaplely to converge in the zero-sum case (a result we give extend slightly here), does not converge in the general-sum case.

Michael Kearns, Michael L. Littman, Satinder Singh

In this work, we introduce graphical modelsfor multi-player game theory, and give powerful algorithms for computing their Nash equilibria in certain cases. An n-player game is given by an undirected graph on n nodes and a set of n local matrices. The interpretation is that the payoff to player i is determined entirely by the actions of player i and his neighbors in the graph, and thus the payoff matrix to player i is indexed only by these players. We thus view the global n-player game as being composed of interacting local games, each involving many fewer players. Each player's action may have global impact, but it occurs through the propagation of local influences.Our main technical result is an efficient algorithm for computing Nash equilibria when the underlying graph is a tree (or can be turned into a tree with few node mergings). The algorithm runs in time polynomial in the size of the representation (the graph and theassociated local game matrices), and comes in two related but distinct flavors. The first version involves an approximation step, and computes a representation of all approximate Nash equilibria (of which there may be an exponential number in general). The second version allows the exact computation of Nash equilibria at the expense of weakened complexity bounds. The algorithm requires only local message-passing between nodes (and thus can be implemented by the players themselves in a distributed manner). Despite an analogy to inference in Bayes nets that we develop, the analysis of our algorithm is more involved than that for the polytree algorithm in, owing partially to the fact that we must either compute, or select from, an exponential number of potential solutions. We discuss a number of extensions, such as the computation of equilibria with desirable global properties (e.g. maximizing global return), and directions for further research.

Satinder Singh, Michael James, Matthew Rudary

Modeling dynamical systems, both for control purposes and to make predictions about their behavior, is ubiquitous in science and engineering. Predictive state representations (PSRs) are a recently introduced class of models for discrete-time dynamical systems. The key idea behind PSRs and the closely related OOMs (Jaeger's observable operator models) is to represent the state of the system as a set of predictions of observable outcomes of experiments one can do in the system. This makes PSRs rather different from history-based models such as nth-order Markov models and hidden-state-based models such as HMMs and POMDPs. We introduce an interesting construct, the systemdynamics matrix, and show how PSRs can be derived simply from it. We also use this construct to show formally that PSRs are more general than both nth-order Markov models and HMMs/POMDPs. Finally, we discuss the main difference between PSRs and OOMs and conclude with directions for future work.

Ruggiero Cavallo, David C. Parkes, Satinder Singh

Consider a multi-agent system in a dynamic and uncertain environment. Each agent's local decision problem is modeled as a Markov decision process (MDP) and agents must coordinate on a joint action in each period, which provides a reward to each agent and causes local state transitions. A social planner knows the model of every agent's MDP and wants to implement the optimal joint policy, but agents are self-interested and have private local state. We provide an incentive-compatible mechanism for eliciting state information that achieves the optimal joint plan in a Markov perfect equilibrium of the induced stochastic game. In the special case in which local problems are Markov chains and agents compete to take a single action in each period, we leverage Gittins allocation indices to provide an efficient factored algorithm and distribute computation of the optimal policy among the agents. Distributed, optimal coordinated learning in a multi-agent variant of the multi-armed bandit problem is obtained as a special case.

Quang Duong, Michael P. Wellman, Satinder Singh

A graphical multiagent model (GMM) represents a joint distribution over the behavior of a set of agents. One source of knowledge about agents' behavior may come from gametheoretic analysis, as captured by several graphical game representations developed in recent years. GMMs generalize this approach to express arbitrary distributions, based on game descriptions or other sources of knowledge bearing on beliefs about agent behavior. To illustrate the flexibility of GMMs, we exhibit game-derived models that allow probabilistic deviation from equilibrium, as well as models based on heuristic action choice. We investigate three different methods of integrating these models into a single model representing the combined knowledge sources. To evaluate the predictive performance of the combined model, we treat as actual outcome the behavior produced by a reinforcement learning process. We find that combining the two knowledge sources, using any of the methods, provides better predictions than either source alone. Among the combination methods, mixing data outperforms the opinion pool and direct update methods investigated in this empirical trial.