Stochastic and deterministic policy gradients are identical for Gaussian-noise, quadratic-cost continuous control, and any stochastic-policy MDP can be converted into an equivalent deterministic-policy MDP.
Todorov, Lineary-solvable Markov decision problems
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Equivalence of stochastic and deterministic policy gradients
Stochastic and deterministic policy gradients are identical for Gaussian-noise, quadratic-cost continuous control, and any stochastic-policy MDP can be converted into an equivalent deterministic-policy MDP.