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Fukumizu, Kenji (Ed.)While the identification of nonlinear dynamical systems is a fundamental building block of modelbased reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and actions or for systems that can be identified from data generated by i.i.d. random inputs. Nonetheless, many interesting dynamical systems have continuous states and actions and can only be identified through a judicious choice of inputs. Motivated by practical settings, we study a class of nonlinear dynamical systems whose state transitions depend linearly on a known feature embedding of stateaction pairs. To estimate such systems in finitemore »Free, publiclyaccessible full text available February 22, 2023

Banerjee, Arindam ; Fukumizu, Kenji (Ed.)We study a constrained contextual linear bandit setting, where the goal of the agent is to produce a sequence of policies, whose expected cumulative reward over the course of multiple rounds is maximum, and each one of them has an expected cost below a certain threshold. We propose an upperconfidence bound algorithm for this problem, called optimistic pessimistic linear bandit (OPLB), and prove a sublinear bound on its regret that is inversely proportional to the difference between the constraint threshold and the cost of a known feasible action. Our algorithm balances exploration and constraint satisfaction using a novel idea thatmore »

Banerjee, Arindam ; Fukumizu, Kenji (Ed.)

Banerjee, Arindam ; Fukumizu, Kenji (Ed.)

Banerjee, Arindam ; Fukumizu, Kenji (Ed.)

Banerjee, Arindam ; Fukumizu, Kenji (Ed.)Numerous tasks in machine learning and artificial intelligence have been modeled as submodular maximization problems. These problems usually involve sensitive data about individuals, and in addition to maximizing the utility, privacy concerns should be considered. In this paper, we study the general framework of nonnegative monotone submodular maximization subject to matroid or knapsack constraints in both offline and online settings. For the offline setting, we propose a differentially private $(1\frac{\kappa}{e})$approximation algorithm, where $\kappa\in[0,1]$ is the total curvature of the submodular set function, which improves upon prior works in terms of approximation guarantee and query complexity under the same privacy budget.more »

Banerjee, Arindam ; Fukumizu, Kenji (Ed.)Couplings play a central role in the analysis of Markov chain Monte Carlo algorithms and appear increasingly often in the algorithms themselves, e.g. in convergence diagnostics, parallelization, and variance reduction techniques. Existing couplings of the MetropolisHastings algorithm handle the proposal and acceptance steps separately and fall short of the upper bound on onestep meeting probabilities given by the coupling inequality. This paper introduces maximal couplings which achieve this bound while retaining the practical advantages of current methods. We consider the properties of these couplings and examine their behavior on a selection of numerical examples.


Banerjee, Arindam ; Fukumizu, Kenji (Ed.)Principal Component Regression (PCR) is a popular method for prediction from data, and is one way to address the socalled multicollinearity problem in regression. It was shown recently that algorithms for PCR such as hard singular value thresholding (HSVT) are also quite robust, in that they can handle data that has missing or noisy covariates. However, such spectral approaches require strong distributional assumptions on which entries are observed. Specifically, every covariate is assumed to be observed with probability (exactly) p, for some value of p. Our goal in this work is to weaken this requirement, and as a step towardsmore »

Banerjee, Arindam ; Fukumizu, Kenji (Ed.)