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4.6 experiments 58 that did not depend on the state, rather than an estimate of the state value function. The time-dependent baseline was computed by averaging the return at each timestep over the trajectories in the batch. Cart-pole The results are averaged across 21 experiments with different random seeds. Results are shown in Figure 8, and indicate that the best results are obtained at intermediate values of the parameters: γ ∈ [0.96, 0.99] and λ ∈ [0.92, 0.99]. Figure 8: Left: learning curves for cart-pole task, using generalized advantage estimation with varying values of λ at γ = 0.99. The fastest policy improvement is obtain by intermediate values of λ in the range [0.92,0.98]. Right: performance after 20 iterations of policy optimization, as γ and λ are varied. White means higher reward. The best results are obtained at intermediate values of both. 3D bipedal locomotion Each trial took about 2 hours to run on a 16-core machine, where the simulation rollouts were parallelized, as were the function, gradient, and matrix-vector-product evaluations used when optimizing the policy and value function. Here, the results are averaged across 9 trials with different random seeds. The best performance is again obtained using intermediate values of γ ∈ [0.99,0.995],λ ∈ [0.96,0.99]. The result after 1000 it- erations is a fast, smooth, and stable gait that is effectively completely stable. We can compute how much “real time” was used for this learning process: 0.01 seconds/timestep × 50000 timesteps/batch × 1000 batches/3600 · 24 seconds/day = 5.8 days. Hence, it is plausible 0 2 4 6 8 Cart-polelearningcurves(atγ=0.99) No VF λ=1.0 λ=0.99 λ=0.98 λ=0.96 λ=0.92 λ=0.84 λ=0.68 λ=0.36 λ=0 10 0 10 20 30 40 50 number of policy iterations costPDF Image | OPTIMIZING EXPECTATIONS: FROM DEEP REINFORCEMENT LEARNING TO STOCHASTIC COMPUTATION GRAPHS
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