We propose and theoretically analyze an approach for planning with an approximate model in reinforcement learning that can reduce the adverse impact of model error. If the model is accurate enough, it accelerates the convergence to the true value function too. One of its key components is the MaxEnt Model Correction (MoCo) procedure that corrects the model's next-state distributions based on a Maximum Entropy density estimation formulation. Based on MoCo, we introduce the Model Correcting Value Iteration (MoCoVI) algorithm, and its sampled-based variant MoCoDyna. We show that MoCoVI and MoCoDyna's convergence can be much faster than the conventional model-free algorithms. Unlike traditional model-based algorithms, MoCoVI and MoCoDyna effectively utilize an approximate model and still converge to the correct value function.

We design a novel algorithm for optimal transport by drawing from the entropic optimal transport, mirror descent and conjugate gradients literatures. Our scalable and GPU parallelizable algorithm is able to compute the Wasserstein distance with extreme precision, reaching relative error rates of $10^{-8}$ without numerical stability issues. Empirically, the algorithm converges to high precision solutions more quickly in terms of wall-clock time than a variety of algorithms including log-domain stabilized Sinkhorn's Algorithm. We provide careful ablations with respect to algorithm and problem parameters, and present benchmarking over upsampled MNIST images, comparing to various recent algorithms over high-dimensional problems. The results suggest that our algorithm can be a useful addition to the practitioner's optimal transport toolkit.

Bisimulation metrics define a distance measure between states of a Markov decision process (MDP) based on a comparison of reward sequences. Due to this property they provide theoretical guarantees in value function approximation. In this work we first prove that bisimulation metrics can be defined via any $p$-Wasserstein metric for $p\geq 1$. Then we describe an approximate policy iteration (API) procedure that uses $\epsilon$-aggregation with $\pi$-bisimulation and prove performance bounds for continuous state spaces. We bound the difference between $\pi$-bisimulation metrics in terms of the change in the policies themselves. Based on these theoretical results, we design an API($\alpha$) procedure that employs conservative policy updates and enjoys better performance bounds than the naive API approach. In addition, we propose a novel trust region approach which circumvents the requirement to explicitly solve a constrained optimization problem. Finally, we provide experimental evidence of improved stability compared to non-conservative alternatives in simulated continuous control.

There is a general trend towards solving problems suited to deep learning with more complex deep learning architectures trained on larger training sets. This requires longer compute times and greater data parallelization or model parallelization. Both data and model parallelism have been historically faster in parameter server architectures, but data parallelism is starting to be faster in ring architectures due to algorithmic improvements. In this paper, we analyze the math behind ring architectures and make an informed adaptation of dynamic scheduling to ring architectures. To do so, we formulate a non-convex, non-linear, NP-hard integer programming problem and a new efficient doubling heuristic for its solution. We build upon Horovod: an open source ring architecture framework over TensorFlow. We show that Horovod jobs have a low cost to stop and restart and that stopping and restarting ring architecture jobs leads to faster completion times. These two facts make dynamic scheduling of ring architecture jobs feasible. Lastly, we simulate a scheduler using these runs and show a more than halving of average job time on some workload patterns.