82,041 research outputs found
Near-Optimal Algorithms for Online Matrix Prediction
In several online prediction problems of recent interest the comparison class
is composed of matrices with bounded entries. For example, in the online
max-cut problem, the comparison class is matrices which represent cuts of a
given graph and in online gambling the comparison class is matrices which
represent permutations over n teams. Another important example is online
collaborative filtering in which a widely used comparison class is the set of
matrices with a small trace norm. In this paper we isolate a property of
matrices, which we call (beta,tau)-decomposability, and derive an efficient
online learning algorithm, that enjoys a regret bound of O*(sqrt(beta tau T))
for all problems in which the comparison class is composed of
(beta,tau)-decomposable matrices. By analyzing the decomposability of cut
matrices, triangular matrices, and low trace-norm matrices, we derive near
optimal regret bounds for online max-cut, online gambling, and online
collaborative filtering. In particular, this resolves (in the affirmative) an
open problem posed by Abernethy (2010); Kleinberg et al (2010). Finally, we
derive lower bounds for the three problems and show that our upper bounds are
optimal up to logarithmic factors. In particular, our lower bound for the
online collaborative filtering problem resolves another open problem posed by
Shamir and Srebro (2011).Comment: 25 page
Online Similarity Prediction of Networked Data from Known and Unknown Graphs
We consider online similarity prediction problems over networked data. We begin by relating this task to the more standard class prediction problem, showing that, given an arbitrary algorithm for class prediction, we can construct an algorithm for similarity prediction with "nearly" the same mistake bound, and vice versa. After noticing that this general construction is computationally infeasible, we target our study to {\em feasible} similarity prediction algorithms on networked data. We initially assume that the network structure is {\em known} to the learner. Here we observe that Matrix Winnow \cite{w07} has a near-optimal mistake guarantee, at the price of cubic prediction time per round. This motivates our effort for an efficient implementation of a Perceptron algorithm with a weaker mistake guarantee but with only poly-logarithmic prediction time. Our focus then turns to the challenging case of networks whose structure is initially {\em unknown} to the learner. In this novel setting, where the network structure is only incrementally revealed, we obtain a mistake-bounded algorithm with a quadratic prediction time per round
Optimal Net-Load Balancing in Smart Grids with High PV Penetration
Mitigating Supply-Demand mismatch is critical for smooth power grid
operation. Traditionally, load curtailment techniques such as Demand Response
(DR) have been used for this purpose. However, these cannot be the only
component of a net-load balancing framework for Smart Grids with high PV
penetration. These grids can sometimes exhibit supply surplus causing
over-voltages. Supply curtailment techniques such as Volt-Var Optimizations are
complex and computationally expensive. This increases the complexity of
net-load balancing systems used by the grid operator and limits their
scalability. Recently new technologies have been developed that enable the
rapid and selective connection of PV modules of an installation to the grid.
Taking advantage of these advancements, we develop a unified optimal net-load
balancing framework which performs both load and solar curtailment. We show
that when the available curtailment values are discrete, this problem is
NP-hard and develop bounded approximation algorithms for minimizing the
curtailment cost. Our algorithms produce fast solutions, given the tight timing
constraints required for grid operation. We also incorporate the notion of
fairness to ensure that curtailment is evenly distributed among all the nodes.
Finally, we develop an online algorithm which performs net-load balancing using
only data available for the current interval. Using both theoretical analysis
and practical evaluations, we show that our net-load balancing algorithms
provide solutions which are close to optimal in a small amount of time.Comment: 11 pages. To be published in the 4th ACM International Conference on
Systems for Energy-Efficient Built Environments (BuildSys 17) Changes from
previous version: Fixed a bug in Algorithm 1 which was causing some min cost
solutions to be misse
Cover Tree Bayesian Reinforcement Learning
This paper proposes an online tree-based Bayesian approach for reinforcement
learning. For inference, we employ a generalised context tree model. This
defines a distribution on multivariate Gaussian piecewise-linear models, which
can be updated in closed form. The tree structure itself is constructed using
the cover tree method, which remains efficient in high dimensional spaces. We
combine the model with Thompson sampling and approximate dynamic programming to
obtain effective exploration policies in unknown environments. The flexibility
and computational simplicity of the model render it suitable for many
reinforcement learning problems in continuous state spaces. We demonstrate this
in an experimental comparison with least squares policy iteration
Shifting Regret, Mirror Descent, and Matrices
We consider the problem of online prediction in changing environments. In this framework the performance of a predictor is evaluated as the loss relative to an arbitrarily changing predictor, whose individual components come from a base class of predictors. Typical results in the literature consider different base classes (experts, linear predictors on the simplex, etc.) separately. Introducing an arbitrary mapping inside the mirror decent algorithm, we provide a framework that unifies and extends existing results. As an example, we prove new shifting regret bounds for matrix prediction problems
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