This paper studies a strategy for data-driven algorithm design for large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general purpose ways. The goal is to arrive at new approaches that can reliably outperform existing solvers in wall-clock time. We focus on solving integer linear programs, and ground our approach in the large neighborhood search (LNS) paradigm, which iteratively chooses a subset of variables to optimize while leaving the remainder fixed. The appeal of LNS is that it can easily use any existing solver as a subroutine, and thus can inherit the benefits of carefully engineered heuristic or complete approaches and their software implementations. We show that one can learn a good neighborhood selector using imitation and reinforcement learning techniques. Through an extensive empirical validation in bounded-time optimization, we demonstrate that our LNS framework can significantly outperform compared to state-of-the-art commercial solvers such as Gurobi.

In Appendix A, we introduce and recall necessary notations for the supplementary material. Appendix D. Appendix C is devoted to the lemmas and proofs for the computational complexity of B.1 Useful Lemmas We first start with the following useful lemmas for the proof of Theorem 1. Lemma 3. The following inequalities are true for all positive x Proof of Lemma 3. (a) It follows from the assumption x This directly leads to the conclusion. The desired inequalities are equivalent to upper and lower bounds for the second term of the RHS. W e have following upper bounds for the optimal solutions of RSOT's dual form, which is Proof of Lemma 5. First, we will show that null u Finally, applying Lemma 5, we obtain the conclusion.B.2 Detailed Proof of Theorem 1 Denoting k Subsequently, the two terms in the right-hand side can be bounded separately as follows. The main idea for deriving this bound comes from the geometric convergence rate (i.e.

Designing and analyzing model-based RL (MBRL) algorithms with guaranteed monotonic improvement has been challenging, mainly due to the interdependence between policy optimization and model learning. Existing discrepancy bounds generally ignore the impacts of model shifts, and their corresponding algorithms are prone to degrade performance by drastic model updating. In this work, we first propose a novel and general theoretical scheme for a non-decreasing performance guarantee of MBRL. Our follow-up derived bounds reveal the relationship between model shifts and performance improvement. These discoveries encourage us to formulate a constrained lower-bound optimization problem to permit the monotonicity of MBRL. A further example demonstrates that learning models from a dynamically-varying number of explorations benefit the eventual returns. Motivated by these analyses, we design a simple but effective algorithm CMLO (Constrained Model-shift Lower-bound Optimization), by introducing an event-triggered mechanism that flexibly determines when to update the model. Experiments show that CMLO surpasses other state-of-the-art methods and produces a boost when various policy optimization methods are employed.

We study bandit convex optimization methods that adapt to the norm of the com-parator, a topic that has only been studied before for its full-information counterpart.

In this paper, we consider the problem of iterative machine teaching, where a teacher provides examples sequentially based on the current iterative learner.