# Linear Least-Squares algorithms for temporal difference learning

- 1996

#### Abstract

We introduce two new temporal diffence (TD) algorithms based on the theory of linear least-squares function approximation. We define an algorithm we call Least-Squares TD (LS TD) for which we prove probability-one convergence when it is used with a function approximator linear in the adjustable parameters. We then define a recursive version of this algorithm, Recursive Least-Squares TD (RLS TD). Although these new TD algorithms require more computation per time-step than do Sutton's TD(λ) algorithms, they are more efficient in a statistical sense because they extract more information from training experiences. We describe a simulation experiment showing the substantial improvement in learning rate achieved by RLS TD in an example Markov prediction problem. To quantify this improvement, we introduce theTD error variance of a Markov chain, ωTD, and experimentally conclude that the convergence rate of a TD algorithm depends linearly on ωTD. In addition to converging more rapidly, LS TD and RLS TD do not have control parameters, such as a learning rate parameter, thus eliminating the possibility of achieving poor performance by an unlucky choice of parameters.

**DOI:**10.1007/BF00114723

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