Engineering topics

Tumer, Kagan

Publications and source records attributed to Tumer, Kagan.

45 records · Page 3

NASA NTRS2001

Linear and Order Statistics Combiners for Pattern Classification

Several researchers have experimentally shown that substantial improvements can be obtained in difficult pattern recognition problems by combining or integrating the outputs of multiple classifiers. This chapter provides an analytical framework to quantify the improvements in classification results due to combining. The results apply to both linear combiners and order statistics combiners. We first show that to a first order approximation, the error rate obtained over and above the Bayes error rate, is directly proportional to the variance of the actual decision boundaries around the Bayes optimum boundary. Combining classifiers in output space reduces this variance, and hence reduces the 'added' error. If N unbiased classifiers are combined by simple averaging. the added error rate can be reduced by a factor of N if the individual errors in approximating the decision boundaries are uncorrelated. Expressions are then derived for linear combiners which are biased or correlated, and the effect of output correlations on ensemble performance is quantified. For order statistics based non-linear combiners, we derive expressions that indicate how much the median, the maximum and in general the i-th order statistic can improve classifier performance. The analysis presented here facilitates the understanding of the relationships among error rates, classifier boundary distributions, and combining in output space. Experimental results on several public domain data sets are provided to illustrate the benefits of combining and to support the analytical results.

Tumer, Kagan↗

NASA NTRS2000

Optimal Wonderful Life Utility Functions in Multi-Agent Systems

The mathematics of Collective Intelligence (COINs) is concerned with the design of multi-agent systems so as to optimize an overall global utility function when those systems lack centralized communication and control. Typically in COINs each agent runs a distinct Reinforcement Learning (RL) algorithm, so that much of the design problem reduces to how best to initialize/update each agent's private utility function, as far as the ensuing value of the global utility is concerned. Traditional team game solutions to this problem assign to each agent the global utility as its private utility function. In previous work we used the COIN framework to derive the alternative Wonderful Life Utility (WLU), and experimentally established that having the agents use it induces global utility performance up to orders of magnitude superior to that induced by use of the team game utility. The WLU has a free parameter (the clamping parameter) which we simply set to zero in that previous work. Here we derive the optimal value of the clamping parameter, and demonstrate experimentally that using that optimal value can result in significantly improved performance over that of clamping to zero, over and above the improvement beyond traditional approaches.

Wolpert, David H.↗

NASA NTRS2000

Optimal Reward Functions in Distributed Reinforcement Learning

We consider the design of multi-agent systems so as to optimize an overall world utility function when (1) those systems lack centralized communication and control, and (2) each agents runs a distinct Reinforcement Learning (RL) algorithm. A crucial issue in such design problems is to initialize/update each agent's private utility function, so as to induce best possible world utility. Traditional 'team game' solutions to this problem sidestep this issue and simply assign to each agent the world utility as its private utility function. In previous work we used the 'Collective Intelligence' framework to derive a better choice of private utility functions, one that results in world utility performance up to orders of magnitude superior to that ensuing from use of the team game utility. In this paper we extend these results. We derive the general class of private utility functions that both are easy for the individual agents to learn and that, if learned well, result in high world utility. We demonstrate experimentally that using these new utility functions can result in significantly improved performance over that of our previously proposed utility, over and above that previous utility's superiority to the conventional team game utility.

Wolpert, David H.↗

NASA NTRS1999

Dimensionality Reduction Through Classifier Ensembles

In data mining, one often needs to analyze datasets with a very large number of attributes. Performing machine learning directly on such data sets is often impractical because of extensive run times, excessive complexity of the fitted model (often leading to overfitting), and the well-known "curse of dimensionality." In practice, to avoid such problems, feature selection and/or extraction are often used to reduce data dimensionality prior to the learning step. However, existing feature selection/extraction algorithms either evaluate features by their effectiveness across the entire data set or simply disregard class information altogether (e.g., principal component analysis). Furthermore, feature extraction algorithms such as principal components analysis create new features that are often meaningless to human users. In this article, we present input decimation, a method that provides "feature subsets" that are selected for their ability to discriminate among the classes. These features are subsequently used in ensembles of classifiers, yielding results superior to single classifiers, ensembles that use the full set of features, and ensembles based on principal component analysis on both real and synthetic datasets.

Oza, Nikunj C.↗

NASA NTRS1999

A Survey of Collective Intelligence

This chapter presents the science of "COllective INtelligence" (COIN). A COIN is a large multi-agent systems where: i) the agents each run reinforcement learning (RL) algorithms; ii) there is little to no centralized communication or control; iii) there is a provided world utility function that, rates the possible histories of tile full system. Tile conventional approach to designing large distributed systems to optimize a world utility does not use agents running RL algorithms. Rather that approach begins with explicit modeling of the overall system's dynamics, followed by detailed hand-tuning of the interactions between the components to ensure that they "cooperate" as far as the world utility is concerned. This approach is labor-intensive, often results in highly non-robust systems, and usually results in design techniques that, have limited applicability. In contrast, with COINs we wish to solve the system design problems implicitly, via the 'adaptive' character of the RL algorithms of each of the agents. This COIN approach introduces an entirely new, profound design problem: Assuming the RL algorithms are able to achieve high rewards, what reward functions for the individual agents will, when pursued by those agents, result in high world utility? In other words, what reward functions will best ensure that we do not have phenomena like the tragedy of the commons, or Braess's paradox? Although still very young, the science of COINs has already resulted in successes in artificial domains, in particular in packet-routing, the leader-follower problem, and in variants of Arthur's "El Farol bar problem". It is expected that as it matures not only will COIN science expand greatly the range of tasks addressable by human engineers, but it will also provide much insight into already established scientific fields, such as economics, game theory, or population biology.

Wolpert, David H.↗

NASA NTRS1999

Avoiding Braess' Paradox Through Collective Intelligence

In an Ideal Shortest Path Algorithm (ISPA), at each moment each router in a network sends all of its traffic down the path that will incur the lowest cost to that traffic. In the limit of an infinitesimally small amount of traffic for a particular router, its routing that traffic via an ISPA is optimal, as far as cost incurred by that traffic is concerned. We demonstrate though that in many cases, due to the side-effects of one router's actions on another routers performance, having routers use ISPA's is suboptimal as far as global aggregate cost is concerned, even when only used to route infinitesimally small amounts of traffic. As a particular example of this we present an instance of Braess' paradox for ISPA'S, in which adding new links to a network decreases overall throughput. We also demonstrate that load-balancing, in which the routing decisions are made to optimize the global cost incurred by all traffic currently being routed, is suboptimal as far as global cost averaged across time is concerned. This is also due to "side-effects", in this case of current routing decision on future traffic. The theory of COllective INtelligence (COIN) is concerned precisely with the issue of avoiding such deleterious side-effects. We present key concepts from that theory and use them to derive an idealized algorithm whose performance is better than that of the ISPA, even in the infinitesimal limit. We present experiments verifying this, and also showing that a machine-learning-based version of this COIN algorithm in which costs are only imprecisely estimated (a version potentially applicable in the real world) also outperforms the ISPA, despite having access to less information than does the ISPA. In particular, this COIN algorithm avoids Braess' paradox.

Wolpert , David H.↗

NASA NTRS1999

Decimated Input Ensembles for Improved Generalization

Recently, many researchers have demonstrated that using classifier ensembles (e.g., averaging the outputs of multiple classifiers before reaching a classification decision) leads to improved performance for many difficult generalization problems. However, in many domains there are serious impediments to such "turnkey" classification accuracy improvements. Most notable among these is the deleterious effect of highly correlated classifiers on the ensemble performance. One particular solution to this problem is generating "new" training sets by sampling the original one. However, with finite number of patterns, this causes a reduction in the training patterns each classifier sees, often resulting in considerably worsened generalization performance (particularly for high dimensional data domains) for each individual classifier. Generally, this drop in the accuracy of the individual classifier performance more than offsets any potential gains due to combining, unless diversity among classifiers is actively promoted. In this work, we introduce a method that: (1) reduces the correlation among the classifiers; (2) reduces the dimensionality of the data, thus lessening the impact of the 'curse of dimensionality'; and (3) improves the classification performance of the ensemble.

Tumer, Kagan↗

NASA NTRS1998

Distributed Control with Collective Intelligence

We consider systems of interacting reinforcement learning (RL) algorithms that do not work at cross purposes , in that their collective behavior maximizes a global utility function. We call such systems COllective INtelligences (COINs). We present the theory of designing COINs. Then we present experiments validating that theory in the context of two distributed control problems: We show that COINs perform near-optimally in a difficult variant of Arthur's bar problem [Arthur] (and in particular avoid the tragedy of the commons for that problem), and we also illustrate optimal performance in the master-slave problem.

Wolpert, David H.↗

NASA NTRS1998

Using Collective Intelligence to Route Internet Traffic

A Collective Intelligence (COIN) is a community of interacting reinforcement learning (RL) algorithms designed so that their collective behavior maximizes a global utility function. We introduce the theory of COINs, then present experiments using that theory to design COINs to control internet traffic routing. These experiments indicate that COINs outperform previous RL-based systems for such routing that have previously been investigated.

Wolpert, David H.↗