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J. Kolter

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6 papers

1 author row

AAAI Conference 2017 Conference Paper

Polynomial Optimization Methods for Matrix Factorization

Po-Wei Wang
Chun-Liang Li
J. Kolter

Matrix factorization is a core technique in many machine learning problems, yet also presents a nonconvex and often difﬁcult-to-optimize problem. In this paper we present an approach based upon polynomial optimization techniques that both improves the convergence time of matrix factorization algorithms and helps them escape from local optima. Our method is based on the realization that given a joint search direction in a matrix factorization task, we can solve the “subspace search” problem (the task of jointly ﬁnding the steps to take in each direction) by solving a bivariate quartic polynomial optimization problem. We derive two methods for solving this problem based upon sum of squares moment relaxations and the Durand-Kerner method, then apply these techniques on matrix factorization to derive a direct coordinate descent approach and a method for speeding up existing approaches. On three benchmark datasets we show the method substantially improves convergence speed over state-of-the-art approaches, while also attaining lower objective value.

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AAAI Conference 2014 Conference Paper

Contextually Supervised Source Separation with Application to Energy Disaggregation

Matt Wytock
J. Kolter

We propose a new framework for single-channel source separation that lies between the fully supervised and unsupervised setting. Instead of supervision, we provide input features for each source signal and use convex methods to estimate the correlations between these features and the unobserved signal decomposition. Contextually supervised source separation is a natural fit for domains with large amounts of data but no explicit supervision; our motivating application is energy disaggregation of hourly smart meter data (the separation of whole-home power signals into different energy uses). Here contextual supervision allows us to provide itemized energy usage for thousands homes, a task previously impossible due to the need for specialized data collection hardware. On smaller datasets which include labels, we demonstrate that contextual supervision improves significantly over a reasonable baseline and existing unsupervised methods for source separation. Finally, we analyze the case of `2 loss theoretically and show that recovery of the signal components depends only on cross-correlation between features for different signals, not on correlations between features for the same signal.

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AAAI Conference 2011 Conference Paper

A Large-Scale Study on Predicting and Contextualizing Building Energy Usage

J. Kolter
Joseph Ferreira

In this paper we present a data-driven approach to modeling end user energy consumption in residential and commercial buildings. Our model is based upon a data set of monthly electricity and gas bills, collected by a utility over the course of several years, for approximately 6, 500 buildings in Cambridge, MA. In addition, we use publicly available tax assessor records and geographical survey information to determine corresponding features for the buildings. Using both parametric and non-parametric learning methods, we learn models that predict distributions over energy usage based upon these features, and use these models to develop two end-user systems. For utilities or authorized institutions (those who may obtain access to the full data) we provide a system that visualizes energy consumption for each building in the city; this allows companies to quickly identify outliers (buildings which use much more energy than expected even after conditioning on the relevant predictors), for instance allowing them to target homes for potential retroﬁts or tiered pricing schemes. For other end users, we provide an interface for entering their own electricity and gas usage, along with basic information about their home, to determine how their consumption compares to that of similar buildings as predicted by our model. Merely allowing users to contextualize their consumption in this way, relating it to the consumption in similar buildings, can itself produce behavior changes to signiﬁcantly reduce consumption.

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NeurIPS Conference 2011 Conference Paper

The Fixed Points of Off-Policy TD

J. Kolter

Off-policy learning, the ability for an agent to learn about a policy other than the one it is following, is a key element of Reinforcement Learning, and in recent years there has been much work on developing Temporal Different (TD) algorithms that are guaranteed to converge under off-policy sampling. It has remained an open question, however, whether anything can be said a priori about the quality of the TD solution when off-policy sampling is employed with function approximation. In general the answer is no: for arbitrary off-policy sampling the error of the TD solution can be unboundedly large, even when the approximator can represent the true value function well. In this paper we propose a novel approach to address this problem: we show that by considering a certain convex subset of off-policy distributions we can indeed provide guarantees as to the solution quality similar to the on-policy case. Furthermore, we show that we can efficiently project on to this convex set using only samples generated from the system. The end result is a novel TD algorithm that has approximation guarantees even in the case of off-policy sampling and which empirically outperforms existing TD methods.

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NeurIPS Conference 2010 Conference Paper

Energy Disaggregation via Discriminative Sparse Coding

J. Kolter
Siddharth Batra
Andrew Ng

Energy disaggregation is the task of taking a whole-home energy signal and separating it into its component appliances. Studies have shown that having device-level energy information can cause users to conserve significant amounts of energy, but current electricity meters only report whole-home data. Thus, developing algorithmic methods for disaggregation presents a key technical challenge in the effort to maximize energy conservation. In this paper, we examine a large scale energy disaggregation task, and apply a novel extension of sparse coding to this problem. In particular, we develop a method, based upon structured prediction, for discriminatively training sparse coding algorithms specifically to maximize disaggregation performance. We show that this significantly improves the performance of sparse coding algorithms on the energy task and illustrate how these disaggregation results can provide useful information about energy usage.

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NeurIPS Conference 2007 Conference Paper

Hierarchical Apprenticeship Learning with Application to Quadruped Locomotion

J. Kolter
Pieter Abbeel
Andrew Ng

We consider apprenticeship learning—learning from expert demonstrations—in the setting of large, complex domains. Past work in apprenticeship learning requires that the expert demonstrate complete trajectories through the domain. However, in many problems even an expert has difﬁculty controlling the system, which makes this approach infeasible. For example, consider the task of teach- ing a quadruped robot to navigate over extreme terrain; demonstrating an optimal policy (i. e. , an optimal set of foot locations over the entire terrain) is a highly non-trivial task, even for an expert. In this paper we propose a method for hier- archical apprenticeship learning, which allows the algorithm to accept isolated advice at different hierarchical levels of the control task. This type of advice is often feasible for experts to give, even if the expert is unable to demonstrate com- plete trajectories. This allows us to extend the apprenticeship learning paradigm to much larger, more challenging domains. In particular, in this paper we apply the hierarchical apprenticeship learning algorithm to the task of quadruped loco- motion over extreme terrain, and achieve, to the best of our knowledge, results superior to any previously published work.

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