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Guided policy search is a popular approach for training controllers forhigh-dimensional systems, but it has a number of pitfalls. Non-convextrajectory optimization has local minima, and non-uniqueness in the optimalpolicy itself can mean that independently-optimized samples do not describe acoherent policy from which to train. We introduce LVIS, which circumvents theissue of local minima through global mixed-integer optimization and the issueof non-uniqueness through learning the optimal value function (or cost-to-go)rather than the optimal policy. To avoid the expense of solving themixed-integer programs to full global optimality, we instead solve them onlypartially, extracting intervals containing the true cost-to-go from earlytermination of the branch-and-bound algorithm. These interval samples are usedto weakly supervise the training of a neural net which approximates the truecost-to-go. Online, we use that learned cost-to-go as the terminal cost of aone-step model-predictive controller, which we solve via a small mixed-integeroptimization. We demonstrate the LVIS approach on a cart-pole system with wallsand a planar humanoid robot model and show that it can be applied to afundamentally hard problem in feedback control--control through contact.

LVIS: Learning from Value Function Intervals for Contact-Aware Robot Controllers