In many real-world hybrid (mixed discrete continuous) planning problems such as Reservoir Control, Heating, Ventilation and Air Conditioning (HVAC), and Navigation, it is difficult to obtain a model of the complex nonlinear dynamics that govern state evolution. However, the ubiquity of modern sensors allow us to collect large quantities of data from each of these complex systems and build accurate, nonlinear deep network models of their state transitions. But there remains one major problem for the task of control -how can we plan with deep network learned transition models without resorting to Monte Carlo Tree Search and other black-box transition model techniques that ignore model structure and do not easily extend to mixed discrete and continuous domains? In this paper, we make the critical observation that the popular Rectified Linear Unit (ReLU) transfer function for deep networks not only allows accurate nonlinear deep net model learning, but also permits a direct compilation of the deep network transition model to a MixedInteger Linear Program (MILP) encoding in a planner we call Hybrid Deep MILP Planning (HD-MILP-PLAN). We identify deep net specific optimizations and a simple sparsification method for HD-MILP-PLAN that improve performance over a naïve encoding, and show that we are able to plan optimally with respect to the learned deep network.
In this paper, we leverage the efficiency of Binarized Neural Networks (BNNs) to learn complex state transition models of planning domains with discretized factored state and action spaces. In order to directly exploit this transition structure for planning, we present two novel compilations of the learned factored planning problem with BNNs based on reductions to Boolean Satisfiability (FD-SAT-Plan) as well as Binary Linear Programming (FD-BLP-Plan). Experimentally, we show the effectiveness of learning complex transition models with BNNs, and test the runtime efficiency of both encodings on the learned factored planning problem. After this initial investigation, we present an incremental constraint generation algorithm based on generalized landmark constraints to improve the planning accuracy of our encodings. Finally, we show how to extend the best performing encoding (FD-BLP-Plan+) beyond goals to handle factored planning problems with rewards.
In many complex planning problems with factored, continuous state and action spaces such as Reservoir Control, Heating Ventilation and Air Conditioning (HVAC), and Navigation domains, it is difficult to obtain a model of the complex nonlinear dynamics that govern state evolution. However, the ubiquity of modern sensors allows us to collect large quantities of data from each of these complex systems and build accurate, nonlinear deep neural network models of their state transitions. But there remains one major problem for the task of control – how can we plan with deep network learned transition models without resorting to Monte Carlo Tree Search and other black-box transition model techniques that ignore model structure and do not easily extend to continuous domains? In this paper, we introduce two types of planning methods that can leverage deep neural network learned transition models: Hybrid Deep MILP Planner (HD-MILP-Plan) and Tensorflow Planner (TF-Plan). In HD-MILP-Plan, we make the critical observation that the Rectified Linear Unit (ReLU) transfer function for deep networks not only allows faster convergence of model learning, but also permits a direct compilation of the deep network transition model to a Mixed-Integer Linear Program (MILP) encoding. Further, we identify deep network specific optimizations for HD-MILP-Plan that improve performance over a base encoding and show that we can plan optimally with respect to the learned deep networks. In TF-Plan, we take advantage of the efficiency of auto-differentiation tools and GPU-based computation where we encode a subclass of purely continuous planning problems as Recurrent Neural Networks and directly optimize the actions through backpropagation. We compare both planners and show that TF-Plan is able to approximate the optimal plans found by HD-MILP-Plan in less computation time. Hence this article offers two novel planners for continuous state and action domains with learned deep neural net transition models: one optimal method (HD-MILP-Plan) and a scalable alternative for large-scale problems (TF-Plan).
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