## An Emphatic Approach to the Problem of Off-policy Temporal-Difference Learning

Richard S. Sutton, A. Rupam Mahmood, Martha White; 17(73):1−29, 2016.

### Abstract

In this paper we introduce the idea of improving the performance of parametric temporal-difference (TD) learning algorithms by selectively emphasizing or de-emphasizing their updates on different time steps. In particular, we show that varying the emphasis of linear TD($\lambda$)'s updates in a particular way causes its expected update to become stable under off-policy training. The only prior model-free TD methods to achieve this with per- step computation linear in the number of function approximation parameters are the gradient-TD family of methods including TDC, GTD($\lambda$), and GQ$\lambda$). Compared to these methods, our emphatic TD($\lambda$) is simpler and easier to use; it has only one learned parameter vector and one step-size parameter. Our treatment includes general state- dependent discounting and bootstrapping functions, and a way of specifying varying degrees of interest in accurately valuing different states.

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