Related papers: Certified Constraint Propagation and Dual Proof An…
Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…
An integer program is called ideal if its continuous relaxation coincides with its convex hull allowing the problem to be solved as a continuous program and offering substantial computational advantages. Proving idealness analytically can…
One strategy for adversarially training a robust model is to maximize its certified radius -- the neighborhood around a given training sample for which the model's prediction remains unchanged. The scheme typically involves analyzing a…
Distributionally robust optimization (DRO) has shown lot of promise in providing robustness in learning as well as sample based optimization problems. We endeavor to provide DRO solutions for a class of sum of fractionals, non-convex…
Chance-constrained programs (CCP) represent a trade-off between conservatism and robustness in optimization. In many CCPs, one optimizes an objective under a probabilistic constraint continuously parameterized by a random vector $\xi$. In…
We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and…
In distributed model predictive control (DMPC), where a centralized optimization problem is solved in distributed fashion using dual decomposition, it is important to keep the number of iterations in the solution algorithm, i.e. the amount…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
Correctness of results from mixed-integer linear programming (MILP) solvers is critical, particularly in the context of applications such as hardware verification, compiler optimization, or machine-assisted theorem proving. To this end,…
The possibility of errors in human-engineered formal verification software, such as model checkers, poses a serious threat to the purpose of these tools. An established approach to mitigate this problem are certificates -- lightweight,…
Recent works have developed several methods of defending neural networks against adversarial attacks with certified guarantees. However, these techniques can be computationally costly due to the use of certification during training. We…
Probing is an important presolving technique in mixed-integer programming solvers. It selects binary variables, tentatively fixes them to 0 and 1, and performs propagation to deduce additional variable fixings, bound tightenings,…
Efficient implementation of massive multiple-input-multiple-output (MIMO) transceivers is essential for the next-generation wireless networks. To reduce the high computational complexity of the massive MIMO transceiver, in this paper, we…
While Conformal Prediction (CP) has proven to be a powerful framework for uncertainty quantification, guaranteeing conditional coverage remains a central challenge. Although finite-sample, distribution-free conditional validity is known to…
Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…
In this paper we present complexity certification results for a distributed Augmented Lagrangian (AL) algorithm used to solve convex optimization problems involving globally coupled linear constraints. Our method relies on the Accelerated…
Constrained Markov decision processes (CMDPs) are a common way to model safety constraints in reinforcement learning. State-of-the-art methods for efficiently solving CMDPs are based on primal-dual algorithms. For these algorithms, all…
In safety-critical applications that rely on the solution of an optimization problem, the certification of the optimization algorithm is of vital importance. Certification and suboptimality results are available for a wide range of…
We introduce a certified pruning framework that consolidates the principles of counterfactual consistency and their networked extensions into a single operational model, with consequences for both quantum foundations and cryptographic…
We study multiprover interactive proof systems. The power of classical multiprover interactive proof systems, in which the provers do not share entanglement, was characterized in a famous work by Babai, Fortnow, and Lund (Computational…