  Policy Optimization (PO) is a widely used approach to address continuous
control tasks. In this paper, we introduce the notion of mediator feedback that
frames PO as an online learning problem over the policy space. The additional
available information, compared to the standard bandit feedback, allows reusing
samples generated by one policy to estimate the performance of other policies.
Based on this observation, we propose an algorithm, RANDomized-exploration
policy Optimization via Multiple Importance Sampling with Truncation
(RANDOMIST), for regret minimization in PO, that employs a randomized
exploration strategy, differently from the existing optimistic approaches. When
the policy space is finite, we show that under certain circumstances, it is
possible to achieve constant regret, while always enjoying logarithmic regret.
We also derive problem-dependent regret lower bounds. Then, we extend RANDOMIST
to compact policy spaces. Finally, we provide numerical simulations on finite
and compact policy spaces, in comparison with PO and bandit baselines.
