Merging Decision Transformers: Weight Averaging for Forming Multi-Task Policies

Recent work has shown the promise of creating generalist, transformer-based, models for language, vision, and sequential decision-making problems. To create such models, we generally require centralized training objectives, data, and compute. It is of interest if we can more flexibly create generalist policies by merging together multiple, task-specific, individually trained policies. In this work, we take a preliminary step in this direction through merging, or averaging, subsets of Decision Transformers in parameter space trained on different MuJoCo locomotion problems, forming multi-task models without centralized training. We also demonstrate the importance of various methodological choices when merging policies, such as utilizing common pre-trained initializations, increasing model capacity, and utilizing Fisher information for weighting parameter importance. In general, we believe research in this direction could help democratize and distribute the process that forms multi-task robotics policies. Our implementation is available at https://github.com/daniellawson9999/merging-decision-transformers

Fast algorithm for calculating two-photon absorption spectra

We report a numerical calculation of the two-photon absorption coefficient of electrons in a binding potential using the real-time real-space higher-order difference method. By introducing random vector averaging for the intermediate state, the task of evaluating the two-dimensional time integral is reduced to calculating two one-dimensional integrals. This allows the reduction of the computation load down to the same order as that for the linear response function. The relative advantage of the method compared to the straightforward multi-dimensional time integration is greater for the calculation of non-linear response functions of higher order at higher energy resolution.Comment: 4 pages, 2 figures. It will be published in Phys. Rev. E on 1, March, 199

Learned Multi-Patch Similarity

Estimating a depth map from multiple views of a scene is a fundamental task in computer vision. As soon as more than two viewpoints are available, one faces the very basic question how to measure similarity across >2 image patches. Surprisingly, no direct solution exists, instead it is common to fall back to more or less robust averaging of two-view similarities. Encouraged by the success of machine learning, and in particular convolutional neural networks, we propose to learn a matching function which directly maps multiple image patches to a scalar similarity score. Experiments on several multi-view datasets demonstrate that this approach has advantages over methods based on pairwise patch similarity.Comment: 10 pages, 7 figures, Accepted at ICCV 201

Sliced Multi-Marginal Optimal Transport

Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability in the number of measures, samples and dimensionality. In this work, we propose a multi-marginal optimal transport paradigm based on random one-dimensional projections, whose (generalized) distance we term the sliced multi-marginal Wasserstein distance. To construct this distance, we introduce a characterization of the one-dimensional multi-marginal Kantorovich problem and use it to highlight a number of properties of the sliced multi-marginal Wasserstein distance. In particular, we show that (i) the sliced multi-marginal Wasserstein distance is a (generalized) metric that induces the same topology as the standard Wasserstein distance, (ii) it admits a dimension-free sample complexity, (iii) it is tightly connected with the problem of barycentric averaging under the sliced-Wasserstein metric. We conclude by illustrating the sliced multi-marginal Wasserstein on multi-task density estimation and multi-dynamics reinforcement learning problems