Optimality and Approximation with Policy Gradient Methods in Markov Decision Processes
summary
Softmax tabular policy gradients with exact gradients asymptotically converge to a global optimum (softmax keeps nonzero action mass), but rates are weak; adding entropy-style regularization yields a polynomial finite-time bound with linear dependence on S and A, cubic on horizon and a 1/sqrt(T) rate, and a crucial distribution-mismatch M factor measuring state-density ratios. Switching to natural policy gradient removes the state-mass scaling and gives a dimension-free 1/T-type convergence. Function approximation error enters via a compatible function approximation term that controls final suboptimality.
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chapters (16)
- 0:00Intro
- 2:07Questions of interest
- 2:48Main challenges
- 4:04MDP Preliminaries
- 5:55Policy parameterizations
- 8:05Policy gradient algorithm
- 10:56Policy gradient example: Softmax parameterization
- 17:23Entropy regularization
- 20:17Convergence of Entropy regularized PG
- 27:28A natural solution
- 29:40Proof ideas
- 32:09Restricted parameterizations
- 33:23A closer look at Natural Policy Gradient • NPG performs the update
- 36:56Assumptions on policies
- 44:08Extension to finite samples
- 47:28Looking ahead
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