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BACKGROUND 2.1 markov decision processes 2 A Markov Decision Process (MDP) is a mathematical object that describes an agent in- teracting with a stochastic environment. It is defined by the following components: • S: state space, a set of states of the environment. • A: action space, a set of actions, which the agent selects from at each timestep. • P(r, s′ | s, a): a transition probability distribution. For each state s and action a, P specifies the probability that the environment will emit reward r and transition to state s′. In certain problem settings, we will also be concerned with an initial state distribution μ(s), which is the probability distribution that the initial state s0 is sampled from. Various different definitions of MDP are used throughout the literature. Sometimes, the reward is defined as a deterministic function R(s), R(s, a), or R(s, a, s′). These formu- lations are equivalent in expressive power. That is, given a deterministic-reward formu- lation, we can simulate a stochastic reward by lumping the reward into the state. The end goal is to find a policy π, which maps states to actions. We will mostly con- sider stochastic policies, which are conditional distributions π(a | s), though elsewhere in the literature, one frequently sees deterministic policies a = π(s). 2.2 the episodic reinforcement learning problem This thesis will be focused on the episodic setting of reinforcement learning, where the agent’s experience is broken up into a series of episodes—sequences with a finite num- ber of states, actions and rewards. Episodic reinforcement learning in the fully-observed setting is defined by the following process. Each episode begins by sampling an initial state of the environment, s0, from distribution μ(s0). Each timestep t = 0,1,2,..., the 8PDF Image | OPTIMIZING EXPECTATIONS: FROM DEEP REINFORCEMENT LEARNING TO STOCHASTIC COMPUTATION GRAPHS
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