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While mixed integer linear programming (MILP) solvers are routinely used to solve a wide range of important science and engineering problems, it remains a challenging task for end users to write correct and efficient MILP constraints, especially for problems specified using the inherently non-linear Boolean logic operations. To overcome this challenge, we propose a syntax guided synthesis (SyGuS) method capable of generating high-quality MILP constraints from the specifications expressed using arbitrary combinations of Boolean logic operations. At the center of our method is an extensible domain specification language (DSL) whose expressiveness may be improved by adding new integer variables as decision variables, together with an iterative procedure for synthesizing linear constraints from non-linear Boolean logic operations using these integer variables. To make the synthesis method efficient, we also propose an over-approximation technique for soundly proving the correctness of the synthesized linear constraints, and an under-approximation technique for safely pruning away the incorrect constraints. We have implemented and evaluated the method on a wide range of benchmark specifications from statistics, machine learning, and data science applications. The experimental results show that the method is efficient in handling these benchmarks, and the quality of the synthesized MILP constraints is close to, or higher than, that of manually-written constraints in terms of both compactness and solving time.
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Learning from Demonstrations under Stochastic Temporal Logic Constraints
We address the problem of learning from demonstrations when the learner must satisfy safety and/or performance requirements expressed as Stochastic Temporal Logic (StTL) specifications. We extend the maximum causal entropy inverse reinforcement learning framework to account for StTL constraints and show how to encode them via a minimal set of mixed-integer linear constraints. Our method is based on a cut-and-generate algorithm that iterates between two phases: in the cut phase, we use cutting hyperplanes to approximate the feasible region of the non-linear constraint that encodes atomic predicates and in the generate phase, we propagate these hyperplanes through the schematics to generate constraints for arbitrary formulas. Our algorithmic contributions are validated in different environments and specifications.
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- Award ID(s):
- 1932620
- PAR ID:
- 10380952
- Date Published:
- Journal Name:
- 2022 American Control Conference (ACC)
- Volume:
- 2022
- Page Range / eLocation ID:
- 2598 to 2603
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ACC53348.2022.9867861
