Algorithm Portfolios for Noisy Optimization

Noisy optimization is the optimization of objective functions corrupted by noise. A portfolio of solvers is a set of solvers equipped with an algorithm selection tool for distributing the computational power among them. Portfolios are widely and successfully used in combinatorial optimization. In this work, we study portfolios of noisy optimization solvers. We obtain mathematically proved performance (in the sense that the portfolio performs nearly as well as the best of its solvers) by an ad hoc portfolio algorithm dedicated to noisy optimization. A somehow surprising result is that it is better to compare solvers with some lag, i.e., propose the current recommendation of best solver based on their performance earlier in the run. An additional finding is a principled method for distributing the computational power among solvers in the portfolio.Comment: in Annals of Mathematics and Artificial Intelligence, Springer Verlag, 201

A Conceptual Model of Investor Behavior

Based on a survey of behavioral finance literature, this paper presents a descriptive model of individual investor behavior in which investment decisions are seen as an iterative process of interactions between the investor and the investment environment. This investment process is influenced by a number of interdependent variables and driven by dual mental systems, the interplay of which contributes to boundedly rational behavior where investors use various heuristics and may exhibit behavioral biases. In the modeling tradition of cognitive science and intelligent systems, the investor is seen as a learning, adapting, and evolving entity that perceives the environment, processes information, acts upon it, and updates his or her internal states. This conceptual model can be used to build stylized representations of (classes of) individual investors, and further studied using the paradigm of agent-based artificial financial markets. By allowing us to implement individual investor behavior, to choose various market mechanisms, and to analyze the obtained asset prices, agent-based models can bridge the gap between the micro level of individual investor behavior and the macro level of aggregate market phenomena. It has been recognized, yet not fully explored, that these models could be used as a tool to generate or test various behavioral hypothesis.behavioral finance;financial decision making;agent-based artificial financial markets;cognitive modeling;investor behavior

Approximate Convex Optimization by Online Game Playing

Lagrangian relaxation and approximate optimization algorithms have received much attention in the last two decades. Typically, the running time of these methods to obtain a $\epsilon$ approximate solution is proportional to $\frac{1}{\epsilon^2}$. Recently, Bienstock and Iyengar, following Nesterov, gave an algorithm for fractional packing linear programs which runs in $\frac{1}{\epsilon}$ iterations. The latter algorithm requires to solve a convex quadratic program every iteration - an optimization subroutine which dominates the theoretical running time. We give an algorithm for convex programs with strictly convex constraints which runs in time proportional to $\frac{1}{\epsilon}$. The algorithm does NOT require to solve any quadratic program, but uses gradient steps and elementary operations only. Problems which have strictly convex constraints include maximum entropy frequency estimation, portfolio optimization with loss risk constraints, and various computational problems in signal processing. As a side product, we also obtain a simpler version of Bienstock and Iyengar's result for general linear programming, with similar running time. We derive these algorithms using a new framework for deriving convex optimization algorithms from online game playing algorithms, which may be of independent interest

An Entropy Search Portfolio for Bayesian Optimization

Bayesian optimization is a sample-efficient method for black-box global optimization. How- ever, the performance of a Bayesian optimization method very much depends on its exploration strategy, i.e. the choice of acquisition function, and it is not clear a priori which choice will result in superior performance. While portfolio methods provide an effective, principled way of combining a collection of acquisition functions, they are often based on measures of past performance which can be misleading. To address this issue, we introduce the Entropy Search Portfolio (ESP): a novel approach to portfolio construction which is motivated by information theoretic considerations. We show that ESP outperforms existing portfolio methods on several real and synthetic problems, including geostatistical datasets and simulated control tasks. We not only show that ESP is able to offer performance as good as the best, but unknown, acquisition function, but surprisingly it often gives better performance. Finally, over a wide range of conditions we find that ESP is robust to the inclusion of poor acquisition functions.Comment: 10 pages, 5 figure

Joint Channel Selection and Power Control in Infrastructureless Wireless Networks: A Multi-Player Multi-Armed Bandit Framework

This paper deals with the problem of efficient resource allocation in dynamic infrastructureless wireless networks. Assuming a reactive interference-limited scenario, each transmitter is allowed to select one frequency channel (from a common pool) together with a power level at each transmission trial; hence, for all transmitters, not only the fading gain, but also the number of interfering transmissions and their transmit powers are varying over time. Due to the absence of a central controller and time-varying network characteristics, it is highly inefficient for transmitters to acquire global channel and network knowledge. Therefore a reasonable assumption is that transmitters have no knowledge of fading gains, interference, and network topology. Each transmitting node selfishly aims at maximizing its average reward (or minimizing its average cost), which is a function of the action of that specific transmitter as well as those of all other transmitters. This scenario is modeled as a multi-player multi-armed adversarial bandit game, in which multiple players receive an a priori unknown reward with an arbitrarily time-varying distribution by sequentially pulling an arm, selected from a known and finite set of arms. Since players do not know the arm with the highest average reward in advance, they attempt to minimize their so-called regret, determined by the set of players' actions, while attempting to achieve equilibrium in some sense. To this end, we design in this paper two joint power level and channel selection strategies. We prove that the gap between the average reward achieved by our approaches and that based on the best fixed strategy converges to zero asymptotically. Moreover, the empirical joint frequencies of the game converge to the set of correlated equilibria. We further characterize this set for two special cases of our designed game

Nonrational Actors and Financial Market Behavior

The insights of descriptive decision theorists and psychologists, we believe, have much to contribute to our understanding of financial market macrophenomena. We propose an analytic agenda that distinguishes those individual idiosyncrasies that prove consequential at the macro-level from those that are neutralized by market processes such as poaching. We discuss five behavioral traits - barn-door closing, expert/reliance effects, status quo bias, framing, and herding - that we employ in explaining financial flows. Patterns in flows to mutual funds, to new equities, across national boundaries, as well as movements in debt-equity ratios are shown to be consistent with deviations from rationality.