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Understanding the Effect of Stochasticity in Policy Optimization

Chenjun Xiao
Jincheng Mei


We study stochastic policy optimization in the on-policy case and make the following four contributions. \textit{First}, we show that the ordering of optimization algorithms by their efficiency gets reversed when they have or they not to the true gradient information. In particular, this finding implies that, unlike in the true gradient scenario, geometric information cannot be easily exploited without detrimental consequences in stochastic policy optimization. \textit{Second}, to explain these findings we introduce the concept of \textit{committal rate} for stochastic policy optimization, and show that this can serve as a criterion for determining almost sure convergence to global optimality. \textit{Third}, we show that if there is no external mechanism that allows an algorithm to determine the difference between optimal and sub-optimal actions using only on-policy samples, then there must be an inherent trade-off between exploiting geometry to accelerate convergence versus achieving optimality almost surely. That is, an algorithm either converges to a globally optimal policy with probability $1$ but at a rate no better than $O(1/t)$, or it achieves a faster than $O(1/t)$ convergence rate but then must fail to converge to the globally optimal deterministic policy with some positive probability. \textit{Finally}, we use our committal rate theory to explain why practical policy optimization methods are sensitive to random initialization, and how an ensemble method with parallelism can be guaranteed to achieve near-optimal solutions with high probability.

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