Autoregressive neural language models (LMs) generate a probability distribution over tokens at each time step given a prompt. In this work, we attempt to systematically understand the probability distributions that LMs can produce, showing that some distributions are significantly harder to elicit than others. Specifically, for any target next-token distribution over the vocabulary, we attempt to find a prompt that induces the LM to output a distribution as close as possible to the target, using either soft or hard gradient-based prompt tuning. We find that (1) in general, distributions with very low or very high entropy are easier to approximate than those with moderate entropy; (2) among distributions with the same entropy, those containing ''outlier tokens'' are easier to approximate; (3) target distributions generated by LMs -- even LMs with different tokenizers -- are easier to approximate than randomly chosen targets. These results offer insights into the expressiveness of LMs and the challenges of using them as probability distribution proposers.

Abstract-- Learning a locomotion controller for a musculoskeletal system is challenging due to over-actuation and highdimensional action space. While many reinforcement learning methods attempt to address this issue, they often struggle to learn human-like gaits because of the complexity involved in engineering an effective reward function. In this paper, we demonstrate that adversarial imitation learning can address this issue by analyzing key problems and providing solutions using both current literature and novel techniques. I. INTRODUCTION Locomotion on simulated musculoskeletal humanoids requires precise muscle activation patterns. Humanoid model with 16 DOFs actuated by 92 Muscle-Tendon Units during running (left) and walking (right).

Soft Actor-Critic (SAC) is considered the state-of-the-art algorithm in continuous action space settings. It uses the maximum entropy framework for efficiency and stability, and applies a heuristic temperature Lagrange term to tune the temperature $\alpha$, which determines how "soft" the policy should be. It is counter-intuitive that empirical evidence shows SAC does not perform well in discrete domains. In this paper we investigate the possible explanations for this phenomenon and propose Target Entropy Scheduled SAC (TES-SAC), an annealing method for the target entropy parameter applied on SAC. Target entropy is a constant in the temperature Lagrange term and represents the target policy entropy in discrete SAC. We compare our method on Atari 2600 games with different constant target entropy SAC, and analyze on how our scheduling affects SAC.

Abstract-- Deep reinforcement learning suggests the promise of fully automated learning of robotic control policies that directly map sensory inputs to low-level actions. However, applying deep reinforcement learning methods on real-world robots is exceptionally difficult, due both to the sample complexity and,just as importantly, the sensitivity of such methods to hyperparameters. While hyperparameter tuning can be performed in parallel in simulated domains, it is usually impractical to tune hyperparameters directly on real-world robotic platforms, especially legged platforms like quadrupedal robots that can be damaged through extensive trial-and-error learning. In this paper, we develop a stable variant of the soft actor-critic deep reinforcement learning algorithm that requires minimal hyperparameter tuning, while also requiring only a modest number of trials to learn multilayer neural network policies. This algorithm is based on the framework of maximum entropy reinforcement learning, and automatically trades off exploration against exploitation by dynamically and automatically tuning a temperature parameter that determines the stochasticity of the policy. We show that this method achieves state-of-the-art performance on four standard benchmark environments.We then demonstrate that it can be used to learn quadrupedal locomotion gaits on a real-world Minitaur robot, learning to walk from scratch directly in the real world in two hours of training. I. INTRODUCTION Deep reinforcement learning can be used to automate the acquisition of controllers for a range of robotic tasks, enabling end-to-end learning of policies that map sensory inputs to lowlevel actions.This can be particularly appealing in the domain of robotic locomotion, where manual gait design can be difficult and highly robot-specific.