scholarly journals Temporal Difference Methods for General Projected Equations

2011 ◽  
Vol 56 (9) ◽  
pp. 2128-2139 ◽  
Author(s):  
Dimitri P. Bertsekas
Keyword(s):  
Temporal Difference ◽  
Difference Methods ◽  
Temporal Difference Methods

scholarly journals A Tale of Two-Timescale Reinforcement Learning with the Tightest Finite-Time Bound

2020 ◽  
Vol 34 (04) ◽  
pp. 3701-3708
Author(s):  
Gal Dalal ◽  
Balazs Szorenyi ◽  
Gugan Thoppe
Keyword(s):  
Reinforcement Learning ◽  
Convergence Rate ◽  
Policy Evaluation ◽  
Finite Time ◽  
High Probability ◽  
Temporal Difference ◽  
Time Analysis ◽  
Difference Methods ◽  
Temporal Difference Methods ◽  
Two Timescale Stochastic Approximation

Policy evaluation in reinforcement learning is often conducted using two-timescale stochastic approximation, which results in various gradient temporal difference methods such as GTD(0), GTD2, and TDC. Here, we provide convergence rate bounds for this suite of algorithms. Algorithms such as these have two iterates, θn and wn, which are updated using two distinct stepsize sequences, αn and βn, respectively. Assuming αn = n−α and βn = n−β with 1 > α > β > 0, we show that, with high probability, the two iterates converge to their respective solutions θ* and w* at rates given by ∥θn - θ*∥ = Õ(n−α/2) and ∥wn - w*∥ = Õ(n−β/2); here, Õ hides logarithmic terms. Via comparable lower bounds, we show that these bounds are, in fact, tight. To the best of our knowledge, ours is the first finite-time analysis which achieves these rates. While it was known that the two timescale components decouple asymptotically, our results depict this phenomenon more explicitly by showing that it in fact happens from some finite time onwards. Lastly, compared to existing works, our result applies to a broader family of stepsizes, including non-square summable ones.

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