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Computational game theory has many applications in the modern world in both adversarial situations and the optimization of social good. While there exist many algorithms for computing solutions in two-player interactions, finding optimal…
We propose Scheduled Auxiliary Control (SAC-X), a new learning paradigm in the context of Reinforcement Learning (RL). SAC-X enables learning of complex behaviors - from scratch - in the presence of multiple sparse reward signals. To this…
This paper is about a set-based computing method for solving a general class of two-player zero-sum Stackelberg differential games. We assume that the game is modeled by a set of coupled nonlinear differential equations, which can be…
AlphaZero in 2017 was able to master chess and other games without human knowledge by playing millions of games against itself (self-play), with a computation budget running in the tens of millions of dollars. It used a variant of the Monte…
\emph{Ex ante} correlation is becoming the mainstream approach for \emph{sequential adversarial team games}, where a team of players faces another team in a zero-sum game. It is known that team members' asymmetric information makes both…
This paper introduces MIX, a multi-task deep learning approach to solve open-ended question-answering. First, we design our system as a multi-stage pipeline of 3 building blocks: a BM25-based Retriever to reduce the search space, a…
Many security and other real-world situations are dynamic in nature and can be modelled as strictly competitive (or zero-sum) dynamic games. In these domains, agents perform actions to affect the environment and receive observations --…
We consider the problem of maximizing the minimum (weighted) value of all components of a vector over a polymatroid. This is a special case of the lexicographically optimal base problem introduced and solved by Fujishige. We give an…
This article investigates a fast and stable method to solve Henderson's mixed model equation. The proposed algorithm is stable in that it avoids inverting a matrix of a large dimension and hence is free from the curse of dimensionality.…
The sequential equilibrium is a standard solution concept for extensive-form games with imperfect information that includes an explicit representation of the players' beliefs. An assessment consisting of a strategy and a belief is a…
We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized/regularized least-squares solutions of underdetermined linear equations with nonnegativity variable bounds.…
Parity games play an important role in model checking and synthesis. In their paper, Calude et al. have shown that these games can be solved in quasi-polynomial time. We show that their algorithm can be implemented efficiently: we use their…
We present the bilateral solver, a novel algorithm for edge-aware smoothing that combines the flexibility and speed of simple filtering approaches with the accuracy of domain-specific optimization algorithms. Our technique is capable of…
Deep generative models based on neural differential equations have quickly become the state-of-the-art for numerous generation tasks across many different applications. These models rely on ODE/SDE solvers which integrate from a prior…
A positional game is a game where two players sequentially label vertices of a hypergraph, consisting of a board and a collection of winning sets, with colors assigned to each player until all vertices of the board are claimed. The first…
We introduce, to our knowledge, the first direct second-order method for computing Nash equilibria in two-player zero-sum games. To do so, we construct a Douglas-Rachford-style splitting formulation, which we then solve with a semi-smooth…
We focus on the design of algorithms for finding equilibria in 2-player zero-sum games. Although it is well known that such problems can be solved by a single linear program, there has been a surge of interest in recent years for simpler…
Solving non-linear least-squares problem for pose estimation (rotation and translation) is often a time consuming yet fundamental problem in several real-time computer vision applications. With an adequate rotation parametrization, the…
Higher-dimensional sliding puzzles are constructed on the vertices of a $d$-dimensional hypercube, where $2^d-l$ vertices are distinctly coloured. Rings with the same colours are initially set randomly on the vertices of the hypercube. The…
We give a weak solution for an impartial game we called ``Inverse Treblecross''. We have determined which of its starting positions are $\mathscr{P}$-position and give a reasonable strategy.