相关论文: Numerical solution of a PDE arising from predictio…

We describe an approximate dynamic programming (ADP) approach to compute approximations of the optimal strategies and of the minimal losses that can be guaranteed in discounted repeated games with vector-valued losses. Such games…

Diffusion on complex networks is often modeled as a stochastic process. Yet, recent work on strategic diffusion emphasizes the decision power of agents and treats diffusion as a strategic problem. Here we study the computational aspects of…

We investigate a two-player zero-sum stochastic differential game in which one of the players has more information on the game than his opponent. We show how to construct numerical schemes for the value function of this game, which is given…

We study a variant of decision-theoretic online learning in which the set of experts that are available to Learner can shrink over time. This is a restricted version of the well-studied sleeping experts problem, itself a generalization of…

In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…

A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the a posteriori error estimation framework introduced by…

In the online learning with experts problem, an algorithm must make a prediction about an outcome on each of $T$ days (or times), given a set of $n$ experts who make predictions on each day (or time). The algorithm is given feedback on the…

We study deterministic optimal control problems for differential games with finite horizon. We propose new approximations of the strategies in feedback form, and show error estimates and a convergence result of the value in some weak sense…

A frequently studied performance measure in online optimization is competitive analysis. It corresponds to the worst-case ratio, over all possible inputs of an algorithm, between the performance of the algorithm and the optimal offline…

Deep neural networks (DNNs) are vulnerable to adversarial examples obtained by adding small perturbations to original examples. The added perturbations in existing attacks are mainly determined by the gradient of the loss function with…

This work studies Stackelberg network interdiction games -- an important class of games in which a defender first allocates (randomized) defense resources to a set of critical nodes on a graph while an adversary chooses its path to attack…

We deal with the numerical solution of linear partial differential equations (PDEs) with focus on the goal-oriented error estimates including algebraic errors arising by an inaccurate solution of the corresponding algebraic systems. The…

This paper shows how universal learning can be achieved with expert advice. To this aim, we specify an experts algorithm with the following characteristics: (a) it uses only feedback from the actions actually chosen (bandit setup), (b) it…

In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…

We derive a comparison principle for a degenerate elliptic partial differential equation without boundary conditions which arises naturally in optimal learning strategies. Our argument is direct and exploits the degeneracy of the…

We analyze an online learning algorithm that adaptively combines outputs of two constituent algorithms (or the experts) running in parallel to model an unknown desired signal. This online learning algorithm is shown to achieve (and in some…

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but…

We consider the problem of learning and using predictions for warm start algorithms with predictions. In this setting, an algorithm is given an instance of a problem, and a prediction of the solution. The runtime of the algorithm is bounded…

This article extends the idea of solving parity games by strategy iteration to non-deterministic strategies: In a non-deterministic strategy a player restricts himself to some non-empty subset of possible actions at a given node, instead of…

We investigate the adversarial bandit problem with multiple plays under semi-bandit feedback. We introduce a highly efficient algorithm that asymptotically achieves the performance of the best switching $m$-arm strategy with minimax optimal…