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Q-learning, originally an incremental algorithm for estimating an optimal decision strategy in an infinite-horizon decision problem, now refers to a general class of reinforcement learning methods widely used in statistics and artificial intelligence. In the context of personalized medicine, finite-horizon Q-learning is the workhorse for estimating optimal treatment strategies, known as treatment regimes. Infinite-horizon Q-learning is also increasingly relevant in the growing field of mobile health. In computer science, Q-learning methods have achieved remarkable performance in domains such as game-playing and robotics. In this article, we ( a) review the history of Q-learning in computer science and statistics, ( b) formalize finite-horizon Q-learning within the potential outcomes framework and discuss the inferential difficulties for which it is infamous, and ( c) review variants of infinite-horizon Q-learning and the exploration-exploitation problem, which arises in decision problems with a long time horizon. We close by discussing issues arising with the use of Q-learning in practice, including arguments for combining Q-learning with direct-search methods; sample size considerations for sequential, multiple assignment randomized trials; and possibilities for combining Q-learning with model-based methods.

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Cooperation in settings where agents have both common and conflicting interests (mixed-motive environments) has recently received considerable attention in multiagent learning. However, the mixed-motive environments typically studied have a single cooperative outcome on which all agents can agree. Many real-world multi-agent environments are instead bargaining problems (BPs): they have several Pareto-optimal payoff profiles over which agents have conflicting preferences. We argue that typical cooperation-inducing learning algorithms fail to cooperate in BPs when there is room for normative disagreement resulting in the existence of multiple competing cooperative equilibria, and illustrate this problem empirically. To remedy the issue, we introduce the notion of norm-adaptive policies. Normadaptive policies are capable of behaving according to different norms in different circumstances, creating opportunities for resolving normative disagreement. We develop a class of norm-adaptive policies and show in experiments that these significantly increase cooperation. However, norm-adaptiveness cannot address residual bargaining failure arising from a fundamental tradeoff between exploitability and cooperative robustness.

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