2,276 research outputs found
Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games using Baselines
Learning strategies for imperfect information games from samples of
interaction is a challenging problem. A common method for this setting, Monte
Carlo Counterfactual Regret Minimization (MCCFR), can have slow long-term
convergence rates due to high variance. In this paper, we introduce a variance
reduction technique (VR-MCCFR) that applies to any sampling variant of MCCFR.
Using this technique, per-iteration estimated values and updates are
reformulated as a function of sampled values and state-action baselines,
similar to their use in policy gradient reinforcement learning. The new
formulation allows estimates to be bootstrapped from other estimates within the
same episode, propagating the benefits of baselines along the sampled
trajectory; the estimates remain unbiased even when bootstrapping from other
estimates. Finally, we show that given a perfect baseline, the variance of the
value estimates can be reduced to zero. Experimental evaluation shows that
VR-MCCFR brings an order of magnitude speedup, while the empirical variance
decreases by three orders of magnitude. The decreased variance allows for the
first time CFR+ to be used with sampling, increasing the speedup to two orders
of magnitude
Smoothing Policies and Safe Policy Gradients
Policy gradient algorithms are among the best candidates for the much
anticipated application of reinforcement learning to real-world control tasks,
such as the ones arising in robotics. However, the trial-and-error nature of
these methods introduces safety issues whenever the learning phase itself must
be performed on a physical system. In this paper, we address a specific safety
formulation, where danger is encoded in the reward signal and the learning
agent is constrained to never worsen its performance. By studying actor-only
policy gradient from a stochastic optimization perspective, we establish
improvement guarantees for a wide class of parametric policies, generalizing
existing results on Gaussian policies. This, together with novel upper bounds
on the variance of policy gradient estimators, allows to identify those
meta-parameter schedules that guarantee monotonic improvement with high
probability. The two key meta-parameters are the step size of the parameter
updates and the batch size of the gradient estimators. By a joint, adaptive
selection of these meta-parameters, we obtain a safe policy gradient algorithm
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