ENOT: Expectile Regularization for Fast and Accurate Training of Neural Optimal Transport

We present a new extension for Neural Optimal Transport (NOT) training procedure, capable of accurately and efficiently estimating optimal transportation plan via specific regularisation on conjugate potentials. The main bottleneck of existing NOT solvers is associated with the procedure of finding a near-exact approximation of the conjugate operator (i.e., the c-transform), which is done either by optimizing over maximin objectives or by the computationally-intensive fine-tuning of the initial approximated prediction. We resolve both issues by proposing a new, theoretically justified loss in the form of expectile regularization that enforces binding conditions on the learning dual potentials. Such a regularization provides the upper bound estimation over the distribution of possible conjugate potentials and makes the learning stable, eliminating the need for additional extensive finetuning. We formally justify the efficiency of our method, called Expectile-Regularised Neural Optimal Transport (ENOT). ENOT outperforms previous state-of-the-art approaches on the Wasserstein-2 benchmark tasks by a large margin (up to a 3-fold improvement in quality and up to a 10-fold improvement in runtime).

Align Your Intents: Offline Imitation Learning via Optimal Transport

Offline reinforcement learning (RL) addresses the problem of sequential decision-making by learning optimal policy through pre-collected data, without interacting with the environment. As yet, it has remained somewhat impractical, because one rarely knows the reward explicitly and it is hard to distill it retrospectively. Here, we show that an imitating agent can still learn the desired behavior merely from observing the expert, despite the absence of explicit rewards or action labels. In our method, AILOT (Aligned Imitation Learning via Optimal Transport), we involve special representation of states in a form of intents that incorporate pairwise spatial distances within the data. Given such representations, we define intrinsic reward function via optimal transport distance between the expert's and the agent's trajectories. We report that AILOT outperforms state-of-the art offline imitation learning algorithms on D4RL benchmarks and improves the performance of other offline RL algorithms in the sparse-reward tasks.