On fixed convex combinations of no-regret learners

No-regret algorithms for online convex optimization are potent online learning tools and have been demonstrated to be successful in a wide-ranging number of applications. Considering affine and external regret, we investigate what happens when a set of no-regret learners (voters) merge their respective decisions in each learning iteration to a single, common one in form of a convex combination. We show that an agent (or algorithm) that executes this merged decision in each iteration of the online learning process and each time feeds back a copy of its own reward function to the voters, incurs sublinear regret itself. As a by-product, we obtain a simple method that allows us to construct new no-regret algorithms out of known ones. © 2009 Springer Berlin Heidelberg

Multi-agent planning with mixed-integer programming and adaptive interaction constraint generation (extended abstract)

We consider multi-agent planning in which the agents' optimal plans are solutions to mixed-integer programs (MIP) that are coupled via integer constraints. While in principle, one could find the joint solution by combining the separate problems into one large joint centralized MIP, this approach rapidly becomes intractable for growing numbers of agents and large problem domains. To address this issue, we propose an iterative approach that combines conflict detection with constraint-generation whereby the agents plan repeatedly until all conflicts are resolved. In each planning iteration, the agents plan with as few other agents and interactionconstraints as possible. This yields an optimal method that can reduce computation markedly. We test our approach in the context of multi-agent collision avoidance in graphs with indivisible flows. Our initial simulations on randomized graph routing problems confirm predicted optimality and reduced computational effort. Copyright © 2013, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved

No-regret learning and a mechanism for distributed multiagent planning

We develop a novel mechanism for coordinated, distributed multi-agent planning. We consider problems stated as a collection of single-agent planning problems coupled by common soft constraints on resource consumption. (Resources may be real or fictitious, the latter introduced as a tool for factoring the problem). A key idea is to recast the distributed planning problem as learning in a repeated game between the original agents and a newly introduced group of adversarial agents who influence prices for the resources. The adversarial agents benefit from arbitrage: that is, their incentive is to uncover violations of the resource usage constraints and, by selfishly adjusting prices, encourage the original agents to avoid plans that cause such violations. If all agents employ no-regret learning algorithms in the course of this repeated interaction, we are able to show that our mechanism can achieve design goals such as social optimality (efficiency), budget balance, and Nash-equilibrium convergence to within an error which approaches zero as the agents gain experience. In particular, the agents' average plans converge to a socially optimal solution for the original planning task. We present experiments in a simulated network routing domain demonstrating our method's ability to reliably generate sound plans. Copyright © 2008, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved

Chance constrained model predictive control for multi-agent systems with coupling constraints

We consider stochastic model predictive control of a multi-agent systems with constraints on the probabilities of inter-agent collisions. First, we discuss a method based on sample average approximation of the collision probabilities to make the stochastic control problem computationally tractable. Empirical results indicate that the complexity of the resulting optimization problem can be too high to be solved under realtime requirements. To reduce the computational burden we propose a second approach. It employs probabilistic bounds to determine regions of increased probability of presence for each agent and introduce constraints for the control problem prohibiting overlap of these regions. We prove that the resulting problem is conservative for the original problem, i.e., every control strategy that is feasible under our new constraints will automatically be feasible for the true original problem. Furthermore, we present simulations demonstrating improved run-time performance of our second approach and compare our stochastic method to robust control. © 2012 AACC American Automatic Control Council)

Stochastic processes and feedback-linearisation for online identification and Bayesian adaptive control of fully-actuated mechanical systems

This work proposes a new method for simultaneous probabilistic identification and control of an observable, fully-actuated mechanical system. Identification is achieved by conditioning stochastic process priors on observations of configurations and noisy estimates of configuration derivatives. In contrast to previous work that has used stochastic processes for identification, we leverage the structural knowledge afforded by Lagrangian mechanics and learn the drift and control input matrix functions of the control-affine system separately. We utilise feedback-linearisation to reduce, in expectation, the uncertain nonlinear control problem to one that is easy to regulate in a desired manner. Thereby, our method combines the flexibility of nonparametric Bayesian learning with epistemological guarantees on the expected closed-loop trajectory. We illustrate our method in the context of torque-actuated pendula where the dynamics are learned with a combination of normal and log-normal processes

On the computational benefit of tensor separation for high-dimensional discrete convolutions

Utilizing separation to decompose a local filter mask is a well-known technique to accelerate its convolution with discrete two-dimensional signals such as images. However, many modern days applications involve higher-dimensional, discrete data that needs to be processed but whose inherent spatial complexity would render immediate/naive convolutions computationally infeasible. In this paper, we show how separability of general higher-order tensors can be leveraged to reduce the computational effort for discrete convolutions from super-polynomial to polynomial (in both the filter masks tensor order and spatial expansion). Thus, where applicable, our method compares favorably to current tensor convolution methods and, it renders linear filtering applicable to signal domains whose spatial complexity would otherwise have been prohibitively high. In addition to our theoretical guarantees, we experimentally illustrate our approach to be highly beneficial not only in theory but also in practice. © 2010 Springer Science+Business Media, LLC

Lazy auctions for multi-robot collision avoidance and motion control under uncertainty

We present an auction-flavored multi-robot planning mechanism where coordination is to be achieved on the occupation of atomic resources modeled as binary inter-robot constraints. Introducing virtual obstacles, we show how this approach can be combined with particle-based obstacle avoidance methods, offering a decentralized, auction-based alternative to previously established centralized approaches for multi-robot open-loop control. We illustrate the effectiveness of our new approach by presenting simulations of typical spatially-continuous multi-robot path-planning problems and derive bounds on the collision probability in the presence of uncertainty. © 2012 Springer-Verlag Berlin Heidelberg

EEG-based speech recognition:Impact of temporal effects

In this paper, we investigate the use of electroencephalograhic signals for the purpose of recognizing unspoken speech. The term unspoken speech refers to the process in which a subject imagines speaking a given word without moving any articulatory muscle or producing any audible sound. Early work by Wester (Wester, 2006) presented results which were initially interpreted to be related to brain activity patterns due to the imagination of pronouncing words. However, subsequent investigations lead to the hypothesis that the good recognition performance might instead have resulted from temporal correlated artifacts in the brainwaves since the words were presented in blocks. In order to further investigate this hypothesis, we run a study with 21 subjects, recording 16 EEG channels using a 128 cap montage. The vocabulary consists of 5 words, each of which is repeated 20 times during a recording session in order to train our HMM-based classifier. The words are presented in blockwise, sequential, and random order. We show that the block mode yields an average recognition rate of 45.50%, but it drops to chance level for all other modes. Our experiments suggest that temporal correlated artifacts were recognized instead of words in block recordings and back the above-mentioned hypothesis