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.Comment: 28 page

The acquisition of spanish perfective aspect : A study on children's production and comprehension

This paper presents the acquisition of Spanish perfective aspect in production and comprehension. It argues that, although young children use perfective aspect to talk about completed events, young children have difficulty in assessing perfective meaning from perfective morphology. This paper proposes that in the process of acquiring aspectual meaning, children use local strategies to decode aspectual meaning from form: when analyzing a completed situation, young children depend on certain learnability factors to correctly assess the entailment of completion of the perfective, namely, their ability to determine if the object of the event measures out the event as a whole or not, and their ability to read the agent’s intentions. When those factors are removed from the situation, young children had difficulty determining the entailment of completion of perfective aspect. This study also suggests that the manner in which aspectual information is conveyed in a language, may play a role on the readiness of the acquisition of the semantic morphology of the language (e.g., verb+object vs. verb+affixes). The results of this study indicate that successful performance on the semantics of Spanish perfective aspect develops around the age of 5-6

Robust Taylor rules in an open economy with heterogeneous expectations and least squares learning

The aim of this paper is threefold: (i) to investigate if there is a unique rational expectations equilibrium (REE) in the small open economy in Galí and Monacelli (2005) that is augmented with technical trading in the foreign exchange market; (ii) to investigate if the unique REE is adaptively learnable in a recursive least squares sense; and (iii) to investigate if the unique and adaptively learnable REE is desirable in an inflation rate targeting regime in the sense that a low and not too variable CPI inflation rate in equilibrium is achieved. The monetary authority is using a Taylor rule when setting the nominal interest rate, and we investigate numerically the properties of the model developed. A main conclusion is that the monetary authority should increase (decrease) the interest rate when the CPI inflation rate increases (decreases) and when the currency gets stronger (weaker) to have a desirable rule that is robust with respect to the degree of technical trading in the foreign exchange market. Thus, the value of the currency is a better response variable than the output gap in the most desirable parametrizations of the interest rate rule.determinacy; foreign exchange; inflation rate targeting regime; interest rate rule; robust monetary policy; technical trading

Structure identification in relational data

This paper presents several investigations into the prospects for identifying meaningful structures in empirical data, namely, structures permitting effective organization of the data to meet requirements of future queries. We propose a general framework whereby the notion of identifiability is given a precise formal definition similar to that of learnability. Using this framework, we then explore if a tractable procedure exists for deciding whether a given relation is decomposable into a constraint network or a CNF theory with desirable topology and, if the answer is positive, identifying the desired decomposition. Finally, we address the problem of expressing a given relation as a Horn theory and, if this is impossible, finding the best k-Horn approximation to the given relation. We show that both problems can be solved in time polynomial in the length of the data

NP-hardness of circuit minimization for multi-output functions

Can we design efficient algorithms for finding fast algorithms? This question is captured by various circuit minimization problems, and algorithms for the corresponding tasks have significant practical applications. Following the work of Cook and Levin in the early 1970s, a central question is whether minimizing the circuit size of an explicitly given function is NP-complete. While this is known to hold in restricted models such as DNFs, making progress with respect to more expressive classes of circuits has been elusive. In this work, we establish the first NP-hardness result for circuit minimization of total functions in the setting of general (unrestricted) Boolean circuits. More precisely, we show that computing the minimum circuit size of a given multi-output Boolean function f : {0,1}^n ? {0,1}^m is NP-hard under many-one polynomial-time randomized reductions. Our argument builds on a simpler NP-hardness proof for the circuit minimization problem for (single-output) Boolean functions under an extended set of generators. Complementing these results, we investigate the computational hardness of minimizing communication. We establish that several variants of this problem are NP-hard under deterministic reductions. In particular, unless ? = ??, no polynomial-time computable function can approximate the deterministic two-party communication complexity of a partial Boolean function up to a polynomial. This has consequences for the class of structural results that one might hope to show about the communication complexity of partial functions