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A crucial design decision for any robot learning pipeline is the choice ofpolicy representation: what type of model should be used to generate the nextset of robot actions? Owing to the inherent multi-modal nature of many robotictasks, combined with the recent successes in generative modeling, researchershave turned to state-of-the-art probabilistic models such as diffusion modelsfor policy representation. In this work, we revisit the choice of energy-basedmodels (EBM) as a policy class. We show that the prevailing folklore -- thatenergy models in high dimensional continuous spaces are impractical to train --is false. We develop a practical training objective and algorithm for energymodels which combines several key ingredients: (i) ranking noise contrastiveestimation (R-NCE), (ii) learnable negative samplers, and (iii) non-adversarialjoint training. We prove that our proposed objective function is asymptoticallyconsistent and quantify its limiting variance. On the other hand, we show thatthe Implicit Behavior Cloning (IBC) objective is actually biased even at thepopulation level, providing a mathematical explanation for the poor performanceof IBC trained energy policies in several independent follow-up works. Wefurther extend our algorithm to learn a continuous stochastic process thatbridges noise and data, modeling this process with a family of EBMs indexed byscale variable. In doing so, we demonstrate that the core idea behind recentprogress in generative modeling is actually compatible with EBMs. Altogether,our proposed training algorithms enable us to train energy-based models aspolicies which compete with -- and even outperform -- diffusion models andother state-of-the-art approaches in several challenging multi-modalbenchmarks: obstacle avoidance path planning and contact-rich block pushing.

Revisiting Energy Based Models as Policies: Ranking Noise Contrastive Estimation and Interpolating Energy Models