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4.6 experiments 57 tively. The same architecture was used for the policy and value function. The final output layer had linear activation. The value function estimator used the same architecture, but with only one scalar output. For the simpler cart-pole task, we used a linear policy, and a neural network with one 20-unit hidden layer as the value function. Task details For the cart-pole balancing task, we collected 20 trajectories per batch, with a maximum length of 1000 timesteps, using the physical parameters from Barto, Sutton, and Ander- son [BSA83]. The simulated robot tasks were simulated using the MuJoCo physics engine [TET12]. The humanoid model has 33 state dimensions and 10 actuated degrees of freedom, while the quadruped model has 29 state dimensions and 8 actuated degrees of freedom. The initial state for these tasks consisted of a uniform distribution centered on a reference configuration. We used 50000 timesteps per batch for bipedal locomotion, and 200000 timesteps per batch for quadrupedal locomotion and bipedal standing. Each episode was terminated after 2000 timesteps if the robot had not reached a terminal state beforehand. The timestep was 0.01 seconds. The reward functions are provided in the table below. Task 3D biped locomotion Quadruped locomotion Biped getting up Reward vfwd − 10−5∥u∥2 − 10−5∥fimpact∥2 + 0.2 vfwd − 10−6∥u∥2 − 10−3∥fimpact∥2 + 0.05 −(hhead − 1.5)2 − 10−5∥u∥2 Here, vfwd := forward velocity, u := vector of joint torques, fimpact := impact forces, hhead := height of the head. In the locomotion tasks, the episode is terminated if the center of mass of the actor falls below a predefined height: .8 m for the biped, and .2 m for the quadruped. The constant offset in the reward function encourages longer episodes; otherwise the quadratic reward terms might lead lead to a policy that ends the episodes as quickly as possible. 4.6.3 Experimental Results All results are presented in terms of the cost, which is defined as negative reward and is minimized. Videos of the learned policies are available at https://sites.google.com/ site/gaepapersupp. In plots, “No VF” means that we used a time-dependent baselinePDF Image | OPTIMIZING EXPECTATIONS: FROM DEEP REINFORCEMENT LEARNING TO STOCHASTIC COMPUTATION GRAPHS
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