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Multiple-step lookahead policies have demonstrated high empirical competencein Reinforcement Learning, via the use of Monte Carlo Tree Search or ModelPredictive Control. In a recent work \cite{efroni2018beyond}, multiple-stepgreedy policies and their use in vanilla Policy Iteration algorithms wereproposed and analyzed. In this work, we study multiple-step greedy algorithmsin more practical setups. We begin by highlighting a counter-intuitivedifficulty, arising with soft-policy updates: even in the absence ofapproximations, and contrary to the 1-step-greedy case, monotonic policyimprovement is not guaranteed unless the update stepsize is sufficiently large.Taking particular care about this difficulty, we formulate and analyze onlineand approximate algorithms that use such a multi-step greedy operator.

Multiple-Step Greedy Policies in Online and Approximate Reinforcement Learning