A framework for incremental learning of logic programs

AbstractIn this paper, a framework for incremental learning is proposed. The predicates already learned are used as background knowledge in learning new predicates in this framework. The programs learned in this way have nice modular structure with conceptually separate components. This modularity gives the advantages of portability, reliability and efficient compilation and execution.Starting with a simple idea of Miyano et al. [21,22] for identifying classes of programs which satisfy the condition that all the terms occurring SLD-derivations starting with a query are no bigger than the terms in the initial query, we identify a reasonably big class of polynomial time learnable logic programs. These programs can be learned from a given sequence of examples and a logic program defining the already known predicates. Our class properly contains the class of innermost simple programs of [32] and the class of hereditary programs of [21,22]. Standard programs for gcd, multiplication, quick-sort, reverse and merge are a few examples of programs that can be handled by our results but not by the earlier results of [21,22, 32]

Robustifying Learnability

In recent years, the learnability of rational expectations equilibria (REE) and determinacy of economic structures have rightfully joined the usual performance criteria among the sought after goals of policy design. And while some contributions to the literature (for example Bullard and Mitra (2001) and Evans and Honkapohja (2002)) have made significant headway in establishing certain features of monetary policy rules that facilitate learning, a comprehensive treatment of policy design for learnability has yet to surface, especially for cases in which agents have potentially misspecified their learning models. This paper provides such a treatment. We argue that since even among professional economists a generally acceptable workhorse model of the economy has not been agreed upon, it is unreasonable to expect private agents to have collective rational expectations. We assume instead that agents have an approximate understanding of the workings of the economy and that their task of learning true reduced forms of the economy is subject to potentially destabilizing errors. We then ask: can a central bank set policy that accounts for learning errors but also succeeds in bounding them in a way that allows eventual learnability of the model, given policy. For different parameterizations of a given policy rule applied to a New Keynesian model, we use structured singular value analysis (from robust control) to find the largest ranges of misspecifications that can be tolerated in a learning model without compromising convergence to an REE. A parallel set of experiments seeks to determine the optimal stance (strong inflation as opposed to strong output stabilization) that allows for the greatest scope of errors in learning without leading to expectational instabilty in cases when the central bank designs both optimal and robust policy rules with commitment. We compare the features of all the rules contemplated in the paper with those that maximize economic performance in the true model, and we measure the performance cost of maximizing learnability under the various conditions mentioned here.monetary policy, learning, E-stability, model uncertainty, robustness

When does determinacy imply expectational stability?

In the recent literature on monetary and fiscal policy design, adoption of policies that induce both determinacy and learnability of equilibrium has been considered fundamental to economic stabilization. We study the connections between determinacy of rational expectations equilibrium, and expectational stability or learnability of that equilibrium, in a general class of purely forward-looking models. We ask what types of economic assumptions drive differences in the necessary and sufficient conditions for the two criteria. We apply our result to a relatively general New Keynesian model. Our framework is sufficiently flexible to encompass lags in information, a cost channel for monetary policy, and either Euler equation or infinite horizon approaches to learning. We are able to isolate conditions under which determinacy does and does not imply learnability, and also conditions under which long horizon forecasts make a clear difference to conclusions about expectational stability. The sharpest result is that informational delays break equivalence connections between determinacy and learnability.Rational expectations (Economic theory)

Developments from enquiries into the learnability of the pattern languages from positive data

AbstractThe pattern languages are languages that are generated from patterns, and were first proposed by Angluin as a non-trivial class that is inferable from positive data [D. Angluin, Finding patterns common to a set of strings, Journal of Computer and System Sciences 21 (1980) 46–62; D. Angluin, Inductive inference of formal languages from positive data, Information and Control 45 (1980) 117–135]. In this paper we chronologize some results that developed from the investigations on the inferability of the pattern languages from positive data

Robustifying learnability

In recent years, the learnability of rational expectations equilibria (REE) and determinacy of economic structures have rightfully joined the usual performance criteria among the sought-after goals of policy design. Some contributions to the literature, including Bullard and Mitra (2001) and Evans and Honkapohja (2002), have made significant headway in establishing certain features of monetary policy rules that facilitate learning. However a treatment of policy design for learnability in worlds where agents have potentially misspecified their learning models has yet to surface. This paper provides such a treatment. We begin with the notion that because the profession has yet to settle on a consensus model of the economy, it is unreasonable to expect private agents to have collective rational expectations. We assume that agents have only an approximate understanding of the workings of the economy and that their learning the reduced forms of the economy is subject to potentially destabilizing perturbations. The issue is then whether a central bank can design policy to account for perturbations and still assure the learnability of the model. Our test case is the standard New Keynesian business cycle model. For different parameterizations of a given policy rule, we use structured singular value analysis (from robust control theory) to find the largest ranges of misspecifications that can be tolerated in a learning model without compromising convergence to an REE. In addition, we study the cost, in terms of performance in the steady state of a central bank that acts to robustify learnability on the transition path to REE. (Note: This paper contains full-color graphics) JEL Classification: C6, E5E-stability, learnability, Learning, monetary policy, robust control

Robustifying learnability

In recent years, the learnability of rational expectations equilibria (REE) and determinacy of economic structures have rightfully joined the usual performance criteria among the sought-after goals of policy design. Some contributions to the literature, including Bullard and Mitra (2001) and Evans and Honkapohja (2002), have made significant headway in establishing certain features of monetary policy rules that facilitate learning. However a treatment of policy design for learnability in worlds where agents have potentially misspecified their learning models has yet to surface. This paper provides such a treatment. We begin with the notion that because the profession has yet to settle on a consensus model of the economy, it is unreasonable to expect private agents to have collective rational expectations. We assume that agents have only an approximate understanding of the workings of the economy and that their learning the reduced forms of the economy is subject to potentially destabilizing perturbations. The issue is then whether a central bank can design policy to account for perturbations and still assure the learnability of the model. Our test case is the standard New Keynesian business cycle model. For different parameterizations of a given policy rule, we use structured singular value analysis (from robust control theory) to find the largest ranges of misspecifications that can be tolerated in a learning model without compromising convergence to an REE.Robust control ; Monetary policy

Exact Learning Description Logic Ontologies from Data Retrieval Examples

We investigate the complexity of learning description logic TBoxes in Angluin et al.’s framework of exact learning via queries posed to an oracle. We consider membership queries of the form “is individual a a certain answer to a data retrieval query q of ABox A and the target TBox?” and equivalence queries of the form “is a given TBox equivalent to the target TBox?”. We show that (i) DL-Lite TBoxes with role inclusions and ELI-concept expressions on the right-hand side of inclusions and (ii) EL TBoxes without complex concept expressions on the right-hand side of inclusions can be learned in polynomial time. Both results are proved by a non-trivial reduction to learning from subsumption examples. We also show that arbitrary EL TBoxes cannot be learned in polynomial time

Exact learning description logic ontologies from data retrieval examples

We investigate the complexity of learning description logic ontologies in Angluin et al.'s framework of exact learning via queries posed to an oracle. We consider membership queries of the form "is individual a a certain answer to a data retrieval query q in a given ABox and the unkown target TBox?" and equivalence queries of the form "is a given TBox equivalent to the unknown target TBox?".We show that (i) DL-Lite TBoxes with role inclusions and ELI concept expressions on the right-hand side of inclusions and (ii) EL TBoxes without complex concept expressions on the right-hand side of inclusions can be learned in polynomial time. Both results are proved by a non-trivial reduction to learning from subsumption examples.We also show that arbitrary EL TBoxes cannot be learned in polynomial time