Variational inference (VI) is a specific type of approximate Bayesian inference that approximates an intractable posterior distribution with a tractable one. VI casts the inference problem as an optimization problem, more specifically, the goal is to maximize a lower bound of the logarithm of the marginal likelihood with respect to the parameters of the approximate posterior. Reinforcement learning (RL) on the other hand deals with autonomous agents and how to make them act optimally such as to maximize some notion of expected future cumulative reward. In the non-sequential setting where agents' actions do not have an impact on future states of the environment, RL is covered by contextual bandits and Bayesian optimization. In a proper sequential scenario, however, where agents' actions affect future states, instantaneous rewards need to be carefully traded off against potential long-term rewards. This manuscript shows how the apparently different subjects of VI and RL are linked in two fundamental ways. First, the optimization objective of RL to maximize future cumulative rewards can be recovered via a VI objective under a soft policy constraint in both the non-sequential and the sequential setting. This policy constraint is not just merely artificial but has proven as a useful regularizer in many RL tasks yielding significant improvements in agent performance. And second, in model-based RL where agents aim to learn about the environment they are operating in, the model-learning part can be naturally phrased as an inference problem over the process that governs environment dynamics. We are going to distinguish between two scenarios for the latter: VI when environment states are fully observable by the agent and VI when they are only partially observable through an observation distribution.
翻译:变相推论(VI) 是一种特定类型的贝叶斯推论,它接近于一种棘手的后后院分布,具有可伸缩性。 VI 将推论问题作为一个优化问题,更具体地说,目标是最大限度地降低近似后院参数的边际可能性的对数范围。 另一方面,强化学习(RL) 与自主代理商打交道,以及如何使其最优化地发挥作用,例如最大限度地扩大预期未来累积奖赏的概念。在代理商的行动不会影响未来环境状况的非顺序假设中,RL 被背景强盗和巴伊斯优化所覆盖。 然而,在一个恰当的顺序假设中,如果代理商的行动影响未来状态,则需要谨慎地用潜在的长期奖赏进行交易。 这份手稿表明,显然不同的VI 和RL 的主体是如何在两种基本方式上联系在一起的。 首先,RL 优化目标是通过六级目标,在对未来累积奖赏进行最大程度的评分中,在非后期观测中的软政策约束下, 而在VI 模型中,在正常的排序中, 也就是正常的排序中,这种约束是 。