Related papers: Numerical solution of a PDE arising from predictio…
In this paper, we develop an ensemble-based time-stepping algorithm to efficiently find numerical solutions to a group of linear, second-order parabolic partial differential equations (PDEs). Particularly, the PDE models in the group could…
Multi-agent decision problems are typically solved via distributed iterative algorithms, where the agents only communicate between themselves on a peer-to-peer network. Each agent usually maintains a copy of each decision variable, while…
In zero-sum games, the optimal strategy is well-defined by the Nash equilibrium. However, it is overly conservative when playing against suboptimal opponents and it can not exploit their weaknesses. Limited look-ahead game solving in…
We propose a neural network-based algorithm for solving forward and inverse problems for partial differential equations in unsupervised fashion. The solution is approximated by a deep neural network which is the minimizer of a cost…
Artificial intelligence and robotic competitions are accompanied by a class of game paradigms in which each player privately commits a strategy to a game system which simulates the game using the collected joint strategy and then returns…
Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees. A complementary direction is to develop…
The games of prediction with expert advice are considered in this paper. We present some modification of Kalai and Vempala algorithm of following the perturbed leader for the case of unrestrictedly large one-step gains. We show that in…
This paper considers a variant of the classical online learning problem with expert predictions. Our model's differences and challenges are due to lacking any direct feedback on the loss each expert incurs at each time step $t$. We propose…
We consider the problem of numerically approximating the solutions to a partial differential equation (PDE) when there is insufficient information to determine a unique solution. Our main example is the Poisson boundary value problem, when…
In this paper, we consider linear quadratic team problems with an arbitrary number of quadratic constraints in both stochastic and deterministic settings. The team consists of players with different measurements about the state of nature.…
Learning at the edges has become increasingly important as large quantities of data are continually generated locally. Among others, this paradigm requires algorithms that are simple (so that they can be executed by local devices), robust…
We address the problem of allocating limited resources in a network under persistent yet statistically unknown adversarial attacks. Each node in the network may be degraded, but not fully disabled, depending on its available defensive…
We study two-player general sum repeated finite games where the rewards of each player are generated from an unknown distribution. Our aim is to find the egalitarian bargaining solution (EBS) for the repeated game, which can lead to much…
This paper investigates the problem of Online Convex-Concave Optimization, which extends Online Convex Optimization to two-player time-varying convex-concave games. The goal is to minimize the dynamic duality gap (D-DGap), a critical…
We establish sharp asymptotically optimal strategies for the problem of online prediction with history dependent experts. The prediction problem is played (in part) over a discrete graph called the $d$ dimensional de Bruijn graph, where $d$…
Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through…
In the online matching on the line problem, the task is to match a set of requests $R$ online to a given set of servers $S$. The distance metric between any two points in $R\,\cup\, S$ is a line metric and the objective for the online…
As the dimension of a system increases, traditional methods for control and differential games rapidly become intractable, making the design of safe autonomous agents challenging in complex or team settings. Deep-learning approaches avoid…
Planning in adversarial and uncertain environments can be modeled as the problem of devising strategies in stochastic perfect information games. These games are generalizations of Markov decision processes (MDPs): there are two…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…