42287490
Program Synthesis in the Presence of Infinite Number of Inaccuracies
Most studies modeling inaccurate data in Gold style learning consider cases in which the number of inaccuracies is finite. The present paper argues that this approach is not reasonable for modelling inaccuracies in concepts that are infinite in nature (for example, graphs of computable functions). The effect of an infinite number of inaccuracies in the input data in Gold's model of learning is considered in the context of identification in the limit of computer programs from graphs of computable functions. Three kinds of inaccuracies, namely, noisy data, incomplete data, and imperfect data, are considered. The amount of each of these inaccuracies in the input is measured using certain density notions. A number of interesting hierarchy results are shown based on the densities of inaccuracies present in the input data. Several results establishing trade-offs between the density and type of inaccuracies are also derived.
5851955
Vacillatory Learning of Nearly Minimal Size Grammars
In Gold's influential language learning paradigm a learning machine converges in the limit to one correct grammar. In an attempt to generalize Gold's paradigm, Case considered the question whether people might converge to vacillating between up to (some integer) n > 1 distinct, but equivalent, correct grammars. He showed that larger classes of languages can be algorithmically learned (in the limit) by converging to up to n + 1 rather than up to n correct grammars. He also argued that, for ''small'' n>1, it is plausible that people might sometimes converge to vacillating between up to n grammars. The insistence on small n was motivated by the consideration that, for ''large'' n, at least one of n grammars would be too large to fit in people's heads. Of course, even for Gold's n = 1 case, the single grammar converged to in the limit may be infeasibly large. An interesting complexity restriction to make, then, on the final grammar(s) converged to in the limit is that they all have small size. In this paper we study some of the trade-offs in learning power involved in making a well-defined version of this restriction. We show and exploit as a tool the desirable property that the learning power under our size-restricted criteria (for successful learning) is independent of the underlying acceptable programming systems. We characterize the power of our size-restricted criteria and use this characterization to prove that some classes of languages, which can be learned by converging in the limit to up to n + 1 nearly minimal size correct grammars, cannot be learned by converging to up to n unrestricted grammars even if these latter grammars are allowed to have a finite number of anomalies (i.e., mistakes) per grammar. We also show that there is no loss of learning power in demanding that the final grammars be nearly minimal size iff one is willing to tolerate an unbounded, finite number of anomalies in the final grammars and there is a constant bound on the number of different grammars converged to in the limit. Hence, if we allow an unbounded, finite number of anomalies in the final grammars and the number of different grammars converged to in the limit is unbounded but finite (or if there is a constant bound on the number of anomalies allowed in the final grammars), then there is a loss of learning power in requiring that the final grammars be nearly minimal size. These results do not always match what might be expected from the cases, previously examined by Freivalds, Kinber, and Chen, of learning nearly minimal size programs for functions.
145211
Computational Limits on Team Identification of Languages
A team of learning machines is a multiset of learning machines. A team is said to successfully identify a concept just in case each member of some nonempty subset, of predetermined size, of the team identifies the concept. Team identification of programs for computable functions from their graphs has been investigated by Smith. Pitt showed that this notion is essentially equivalent to function identification by a single probabilistic machine. The present paper introduces, motivates, and studies the more difficult subject of team identification of grammars for languages from positive data. It is shown that an analog of Pitt's result about equivalence of team function identification and probabilistic function identification does not hold for language identification, and the results in the present paper reveal a very complex structure for team language identification. It is also shown that for certain cases probabilistic language identification is strictly more powerful than team language identification. Proofs of many results in the present paper involve very sophisticated diagonalization arguments. Two very general tools are presented that yield proofs of new results from simple arithmetic manipulation of the parameters of known ones.
39847140
Team Learning of Recursive Languages
A team of learning machines is a multiset of learning machines. A team is said to successfully learn a concept just in case each member of some nonempty subset, of predetermined size, of the team learns the concept. Team learning of languages turns out to be a suitable theoretical model for studying computational limits on multi-agent machine learning. Team learning of recursively enumerable languages has been extensively studied. However, it may be argued that from a practical point of view all languages of interest are recursive. 
 
This paper gives theoretical results about team learnability of recursive languages. These results are mainly about two issues: redundancy and aggregation. The issue of redundancy deals with the impact of increasing the size of a team and increasing the number of machines required to be successful. The issue of aggregation deals with conditions under which a team may be replaced by a single machine without any loss in learning ability. The learning scenarios considered are: (a) Identification in the limit of accepting grammars for recursive languages. (b) Identification in the limit of decision procedures for recursive languages. (c) Identification in the limit of accepting grammars for indexed families of recursive languages. (d) Identification in the limit of accepting grammars for indexed families with enumerable class of grammars for the family as the hypothesis space. Scenarios which can be modeled by team learning are also presented.
122230605
On the intrinsic complexity of learning recursive functions
The intrinsic complexity of learning compares the difficulty of learning classes of objects by using some reducibility notion. For several types of learning recursive functions, both natural complete classes are exhibited and necessary and sufficient conditions for completeness are derived. Informally, a class is complete iff both its topological structure is highly complex while its algorithmic structure is easy. Some self-describing classes turn out to be complete. Furthermore, the structure of the intrinsic complexity is shown to be much richer than the structure of the mind change complexity, though in general, intrinsic complexity and mind change complexity can behave "orthogonally".
644359
Anomalous Learning Helps Succinctness
Abstract It is shown that allowing a bounded number of anomalies (mistakes) in the final programs learned by an algorithmic procedure can considerably “succinctify” those final programs. Naturally, only those contexts are investigated in which the presence of anomalies is not actually required for successful inference (learning). The contexts considered are certain infinite subclasses of the class of characteristic functions of finite sets. For each finite set D , these subclasses have a finite set containing D . This latter prevents the anomalies from wiping out all the information in the sets featured in these subclasses and shows the context to be fairly robust. Some of the results in the present paper are shown to be provably more constructive than others. The results of this paper can also be interpreted as facts about succinctness of coding finite sets, which facts have interesting consequences for learnability of decision procedures for finite sets.
14572238
A simulation architecture for manufacturing interoperability testing
Manufacturing systems are often costly to develop and operate. Simulation technology has been demonstrated to be an effective tool for improving the efficiency of manufacturing system design, operation, and maintenance. But manufacturing simulations are usually developed to address a narrow set of industrial issues, e.g., the purchase of new equipment or the modification of a manufacturing process. Once the analysis is complete a particular simulation model may not be used again. If simulations could be made more modular and easily integrated, they could have tremendous value as tools for manufacturing interoperability testing. This paper presents a modular reference architecture to facilitate the integration of manufacturing simulation systems with other support and testing applications. Opportunities for testing are also discussed that will be enabled by the implementation of the architecture.
15127807
Pricing of Information Products on Online Servers: Issues, Models, and Analysis
Online information servers that provide access to diverse databases where users can search for, browse through, and download the information they need have been rapidly increasing in number in the past few years. Online vendors have traditionally charged users for information on the based on the length of the time they were connected to the databases. With hardware and software advances, many online servers have recently started changing their pricing strategies to search-based and/or subscription-fee pricing. This paper examines the various issues involved in pricing these information products, and presents an economic approach to analyze conditions under which the various pricing schemes may prove optimal for the online servers. Our results show that the variation in consumer expertise and valuation of information affects the choice of a pricing strategy by the server. We present general conditions under which subscription-fee pricing is optimal even when consumer demand is inelastic. We also find that, given the cost structures characterizing the market, undifferentiated online servers can compete and coexist in the market each making positive profits. We show that in a competitive setting an increase in costs of online servers can sometimes benefit them by enabling them to differentiate themselves. Our results offer insights into the trends in pricing strategies and may provide an explanation as to why many servers may persist with connect-time strategies.
120386960
Evolutionary games with two timescales
We consider a two timescale model of learning by economic agents wherein active or 'ontogenetic' learning by individuals takes place on a fast scale and passive or 'phylogenetic' learning by society as a whole on a slow scale, each affecting the evolution of the other. The former is modelled by the Monte Carlo dynamics of physics, while the latter is modelled by the replicator dynamics of evolutionary biology. Various qualitative aspects of the dynamics are studied in some simple cases, both analytically and numerically, and its role as a useful modelling device is emphasized.
30649473
Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis
In this paper, we study the name-your-own-price (NYOP) channel. We examine theoretically and empirically whether asking consumers to place a joint bid for multiple items, rather than bid one item at a time as practiced today, can increase NYOP retailers' profits. Relatedly, we also examine whether allowing consumers to self-select whether to place a joint bid or itemwise bids increases retailers' profits and consumers' surplus. We construct a dynamic model that incorporates both demand uncertainty and supply uncertainty to address these issues. Our theoretical analysis identifies the conditions under which joint bidding can increase both NYOP retailers' profits and consumers' surplus. We find that some consumers might bid more for the very same items when they place joint bids. The increase in bid amount is related to the fact that joint bidding reduces the chance of mismatch between NYOP retailers' costs and consumer bids. We conducted a laboratory study to assess the descriptive validity of some of the model predictions, because there are no field data on joint bidding in the NYOP channel. The results of the study are directionally consistent with our theory.
14852497
Towards standards for integrated gaming and simulation for incident management
Simulation and gaming can support decision making through all phases of incident management including prevention, preparedness, response, recovery and mitigation. A number of gaming and simulation tools have been developed for the purpose but they generally utilize proprietary or unique data interfaces and their own view of partitioning the application and solution space. This creates a large obstacle for wide use, and in particular, prevents the use of these tools in an integrated manner to address the application space. This paper explores the groundwork needed to build standards for integrated gaming and simulation tools for incident management. 
 
An architecture has been proposed to identify the required groups of simulation and gaming modules for incident management and define their scope in the solution space. A conceptual model is proposed for the data required for such simulations. Available data exchange standards are mapped to the conceptual data model. A concept prototype has been developed based on the architecture to demonstrate the value of integrated modeling and simulation and the architecture itself. A number of simulation and gaming modules have been utilized to model the major aspects of a hypothetical scenario. The exercise is used to identify the issues due to lack of data exchange standards.