Related papers: Linear Decision Tree Policies for Integer Linear P…
Policy-gradient methods are widely used for learning control policies. They can be easily distributed to multiple workers and reach state-of-the-art results in many domains. Unfortunately, they exhibit large variance and subsequently suffer…
An alphabetic binary tree formulation applies to problems in which an outcome needs to be determined via alphabetically ordered search prior to the termination of some window of opportunity. Rather than finding a decision tree minimizing…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
Reinforcement learning policies are often represented by neural networks, but programmatic policies are preferred in some cases because they are more interpretable, amenable to formal verification, or generalize better. While efficient…
We present a method to solve planning problems involving sequential decision making in unpredictable environments while accomplishing a high level task specification expressed using the formalism of linear temporal logic. Our method…
We propose a novel randomized linear programming algorithm for approximating the optimal policy of the discounted Markov decision problem. By leveraging the value-policy duality and binary-tree data structures, the algorithm adaptively…
We present a self-learning approach for synthesizing programs from integer sequences. Our method relies on a tree search guided by a learned policy. Our system is tested on the On-Line Encyclopedia of Integer Sequences. There, it discovers,…
We study query and computationally efficient planning algorithms with linear function approximation and a simulator. We assume that the agent only has local access to the simulator, meaning that the agent can only query the simulator at…
Mixed-integer programming (MIP) provides a powerful framework for optimization problems, with Branch-and-Cut (B&C) being the predominant algorithm in state-of-the-art solvers. The efficiency of B&C critically depends on heuristic policies…
The ability to compute reward-optimal policies for given and known finite Markov decision processes (MDPs) underpins a variety of applications across planning, controller synthesis, and verification. However, we often want policies (1) to…
With the abundance of available data, many enterprises seek to implement data-driven prescriptive analytics to help them make informed decisions. These prescriptive policies need to satisfy operational constraints, and proactively eliminate…
Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…
It is well known that recurrent sandpile configurations can be characterized as the optimal solution of certain optimization problems. In this article, we present two new integer linear programming models, one that computes recurrent…
One cannot make truly fair decisions using integer linear programs unless one controls the selection probabilities of the (possibly many) optimal solutions. For this purpose, we propose a unified framework when binary decision variables…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We focus on modeling the relationship between an input feature vector and the predicted outcome of a trained decision tree using mixed-integer optimization. This can be used in many practical applications where a decision tree or tree…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired…
High-dimensional policies, such as those represented by neural networks, cannot be reasonably interpreted by humans. This lack of interpretability reduces the trust users have in policy behavior, limiting their use to low-impact tasks such…
This paper deals with the computation of polytopic invariant sets for polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state space such that if the state of the system belongs to the set at a given…