Several techniques have been proposed to tackle the Adaptive Operator Selection (AOS) issue in Evolutionary Algorithms. Some recent proposals are based on the Multi-Armed Bandit (MAB) paradigm: each operator is viewed as one arm of a MAB problem, and the rewards are mainly based on the fitness improvement brought by the corresponding operator to the individual it is applied to. However, the AOS problem is dynamic, whereas standard MAB algorithms are known to optimally solve the exploitation versus exploration trade-off in static settings. An original dynamic variant of the standard MAB Upper Confidence Bound algorithm is proposed here, using a sliding time window to compute both its exploitation and exploration terms. In order to perform sound comparisons between AOS algorithms, artificial scenarios have been proposed in the literature. They are extended here toward smoother transitions between different reward settings. The resulting original testbed also includes a real evolutionary algorithm that is applied to the well-known Royal Road problem. It is used here to perform a thorough analysis of the behavior of AOS algorithms, to assess their sensitivity with respect to their own hyper-parameters, and to propose a sound comparison of their performances.
Credit Assignment is an important ingredient of several proposals that have been made for Adaptive Operator Selection. Instead of the average fitness improvement of newborn offspring, this paper proposes to use some empirical order statistics of those improvements, arguing that rare but highly beneficial jumps matter as much or more than frequent but small improvements. An extreme value based Credit Assignment is thus proposed, rewarding each operator with the best fitness improvement observed in a sliding window for this operator. This mechanism, combined with existing Adaptive Operator Selection rules, is investigated in an EC-like setting. First results show that the proposed method allows both the Adaptive Pursuit and the Dynamic Multi-Armed Bandit selection rules to actually track the best operators along evolution.
Abstract. The performance of many efficient algorithms critically depends on the tuning of their parameters, which on turn depends on the problem at hand. For example, the performance of Evolutionary Algorithms critically depends on the judicious setting of the operator rates. The Adaptive Operator Selection (AOS) heuristic that is proposed here rewards each operator based on the extreme value of the fitness improvement lately incurred by this operator, and uses a Multi-Armed Bandit (MAB) selection process based on those rewards to choose which operator to apply next. This Extreme-based Multi-Armed Bandit approach is experimentally validated against the Average-based MAB method, and is shown to outperform previously published methods, whether using a classical Average-based rewarding technique or the same Extreme-based mechanism. The validation test suite includes the easy One-Max problem and a family of hard problems known as "Long k-paths".
This paper analyses a simple imperfectly competitive general equilibrium model where the entry mechanism generates an endogenous markup. In this second-best world fiscal policy is more effective than in Walrasian or in fixed-markup monopolistic competition models, as it produces efficiency gains through entry.
I develop an intertemporal general equilibrium two-sector model for a small dependent economy. Firms in the non-tradable-good sector are assumed to be large, both at the industry and the economy levels, and to compete over quantities. The exchange rate is ¢xed and ¢nancial capital is perfectly mobile. I study the e¡ects of government purchases of goods on the macroeconomic short-and long-run equilibria when entry is possible. Su¤cient conditions for welfare improvement are also derived.
" IntroductionIn the last decade the analysis of open-economy macroeconomics has shifted from a static framework to an intertemporal one. Simultaneously, macroeconomic models have increasingly incorporated imperfectly competitive structures in order to bypass the limitations of the Walrasian framework. These two features, however, remained separate in international macromodels until the middle of the 1990söas an example see, inter alia, Backus et al. (1994) and Dixon (1994). Even for closed economies, dynamic general equilibrium models with imperfect competition are a recent ¢eld of researchösee inter alia Hairault and Portier (1993) and Rotemberg and Woodford (1995) for some of the earlier references. This paper combines both features following Obstfeld and Rogo¡ (1995). The domestic economy is assumed to be divided in two sectors: one producing a tradable good and the other a non-tradable good. Since the economy is small in the international market for the tradable good, perfect competition holds in its domestic market. As in Dixon (1994), the nontradable-good market is assumed to be imperfectly competitive. However, instead of considering monopolistically competitive markets as in the Dixit and Stiglitz (1977) and Blanchard and Kiyotaki (1987) tradition, size is to the participants at the MMF Conference (Durham), workshops at the universities of Warwick and York, a seminar at ISEG, Technical University of Lisbon, and to two anonymous referees for their comments and suggestions. Faults, of course, remain my own.
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