6 research outputs found
STAMP: Differentiable Task and Motion Planning via Stein Variational Gradient Descent
Planning for many manipulation tasks, such as using tools or assembling
parts, often requires both symbolic and geometric reasoning. Task and Motion
Planning (TAMP) algorithms typically solve these problems by conducting a tree
search over high-level task sequences while checking for kinematic and dynamic
feasibility. This can be inefficient as the width of the tree can grow
exponentially with the number of possible actions and objects. In this paper,
we propose a novel approach to TAMP that relaxes discrete-and-continuous TAMP
problems into inference problems on a continuous domain. Our method, Stein Task
and Motion Planning (STAMP) subsequently solves this new problem using a
gradient-based variational inference algorithm called Stein Variational
Gradient Descent, by obtaining gradients from a parallelized differentiable
physics simulator. By introducing relaxations to the discrete variables,
leveraging parallelization, and approaching TAMP as an Bayesian inference
problem, our method is able to efficiently find multiple diverse plans in a
single optimization run. We demonstrate our method on two TAMP problems and
benchmark them against existing TAMP baselines.Comment: 14 pages, 9 figures, Learning Effective Abstractions for Planning
(LEAP) Workshop at CoRL 202
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Variational methods with dependence structure
It is a common practice among humans to deduce, to explain and to make predictions based on concepts that are not directly observable. In Bayesian statistics, the underlying propositions of the unobserved latent variables are summarized in the posterior distribution. With the increasing complexity of real-world data and statistical models, fast and accurate inference for the posterior becomes essential. Variational methods, by casting the posterior inference problem in the optimization framework, are widely used for their flexibility and computational efficiency. In this thesis, we develop new variational methods, studying their theoretical properties and applications.
In the first part of the thesis, we utilize dependence structures towards addressing fundamental problems in variational inference (VI): posterior uncertainty estimation, convergence properties, and discrete optimization. Though it is flexible, variational inference often underestimates the posterior uncertainty. This is a consequence of the over-simplified variational family. Mean-field variational inference (MFVI), for example, uses a product of independent distributions as a coarse approximation to the posterior. As a remedy, we propose a hierarchical variational distribution with flexible parameterization that can model the dependence structure between latent variables. With a newly derived objective, we show that the proposed variational method can achieve accurate and efficient uncertainty estimation.
We further theoretically study the structured variational inference in the setting of the Stochastic Blockmodel (SBM). The variational distribution is constructed with a pairwise structure among the nodes of a graph. We prove that, in a broad density regime and for general random initializations, the estimated class labels by structured VI converge to the ground truth with high probability. Empirically, we demonstrate structured VI is more robust compared with MFVI when the graph is sparse and the signal to noise ratio is low.
When the latent variables are discrete, gradient descent based VI often suffers from bias and high variance in the gradient estimation. With correlated random samples, we propose a novel unbiased, low-variance gradient estimator. We demonstrate that under certain constraints, such correlated sampling gives an optimal control variates for the variance reduction. The efficient gradient estimation can be applied to solve a wide range of problems such as the variable selection, reinforcement learning, natural language processing, among others.
For the second part of the thesis, we apply variational methods to the study of generalization problems in the meta-learning. When trained over multiple-tasks, we identify that a variety of the meta-learning algorithms implicitly require the tasks to have a mutually-exclusive dependence structure. This prevents the task-level overfitting problem and ensures the fast adaptation of the algorithm in the face of a new task. However, such dependence structure may not exist for general tasks. When the tasks are non-mutually exclusive, we develop new meta-learning algorithms with variational regularization to prevent the task-level overfitting. Consequently, we can expand the meta-learning to the domains which it cannot be effective on before.Statistic