28 research outputs found
Learning Action Models: Qualitative Approach
In dynamic epistemic logic, actions are described using action models. In
this paper we introduce a framework for studying learnability of action models
from observations. We present first results concerning propositional action
models. First we check two basic learnability criteria: finite identifiability
(conclusively inferring the appropriate action model in finite time) and
identifiability in the limit (inconclusive convergence to the right action
model). We show that deterministic actions are finitely identifiable, while
non-deterministic actions require more learning power-they are identifiable in
the limit. We then move on to a particular learning method, which proceeds via
restriction of a space of events within a learning-specific action model. This
way of learning closely resembles the well-known update method from dynamic
epistemic logic. We introduce several different learning methods suited for
finite identifiability of particular types of deterministic actions.Comment: 18 pages, accepted for LORI-V: The Fifth International Conference on
Logic, Rationality and Interaction, October 28-31, 2015, National Taiwan
University, Taipei, Taiwa
Learning and consistency
In designing learning algorithms it seems quite reasonable to construct them in such a way that all data the algorithm already has obtained are correctly and completely reflected in the hypothesis the algorithm outputs on these data. However, this approach may totally fail. It may lead to the unsolvability of the learning problem, or it may exclude any efficient solution of it. Therefore we study several types of consistent learning in recursion-theoretic inductive inference. We show that these types are not of universal power. We give “lower bounds ” on this power. We characterize these types by some versions of decidability of consistency with respect to suitable “non-standard ” spaces of hypotheses. Then we investigate the problem of learning consistently in polynomial time. In particular, we present a natural learning problem and prove that it can be solved in polynomial time if and only if the algorithm is allowed to work inconsistently. 1
A Map of Update Constraints in Inductive Inference
We investigate how different learning restrictions reduce learning power and
how the different restrictions relate to one another. We give a complete map
for nine different restrictions both for the cases of complete information
learning and set-driven learning. This completes the picture for these
well-studied \emph{delayable} learning restrictions. A further insight is
gained by different characterizations of \emph{conservative} learning in terms
of variants of \emph{cautious} learning.
Our analyses greatly benefit from general theorems we give, for example
showing that learners with exclusively delayable restrictions can always be
assumed total.Comment: fixed a mistake in Theorem 21, result is the sam
Combining Models of Approximation with Partial Learning
In Gold's framework of inductive inference, the model of partial learning
requires the learner to output exactly one correct index for the target object
and only the target object infinitely often. Since infinitely many of the
learner's hypotheses may be incorrect, it is not obvious whether a partial
learner can be modifed to "approximate" the target object.
Fulk and Jain (Approximate inference and scientific method. Information and
Computation 114(2):179--191, 1994) introduced a model of approximate learning
of recursive functions. The present work extends their research and solves an
open problem of Fulk and Jain by showing that there is a learner which
approximates and partially identifies every recursive function by outputting a
sequence of hypotheses which, in addition, are also almost all finite variants
of the target function.
The subsequent study is dedicated to the question how these findings
generalise to the learning of r.e. languages from positive data. Here three
variants of approximate learning will be introduced and investigated with
respect to the question whether they can be combined with partial learning.
Following the line of Fulk and Jain's research, further investigations provide
conditions under which partial language learners can eventually output only
finite variants of the target language. The combinabilities of other partial
learning criteria will also be briefly studied.Comment: 28 page
A Note on Batch and Incremental Learnability
AbstractAccording to Gold's criterion of identification in the limit, a learner, presented with data about a concept, is allowed to make a finite number of incorrect hypotheses before converging to a correct hypothesis. If, on the other hand, the learner is allowed to make only one conjecture which has to be correct, the resulting criterion of success is known as finite identification Identification in the limit may be viewed as an idealized model for incremental learning whereas finite identification may be viewed as an idealized model for batch learning. The present paper establishes a surprising fact that the collections of recursively enumerable languages that can be finite identified (batch learned in the ideal case) from both positive and negative data can also be identified in the limit (incrementally learned in the ideal case) from only positive data. It is often difficult to extract insights about practical learning systems from abstract theorems in inductive inference. However, this result may be seen as carrying a moral for the design of learning systems, as it yields, in theidealcase of no inaccuracies, an algorithm for converting batch systems that learn from both positive and negative data into incremental systems that learn from only positive data without any loss in learning power. This is achieved by the incremental system simulating the batch system in incremental fashion and using the heuristic of “localized closed-world assumption” to generate negative data
Towards an Atlas of Computational Learning Theory
A major part of our knowledge about Computational Learning stems from comparisons of the learning power of different learning criteria. These comparisons inform about trade-offs between learning restrictions and, more generally, learning settings; furthermore, they inform about what restrictions can be observed without losing learning power.
With this paper we propose that one main focus of future research in Computational Learning should be on a structured approach to determine the relations of different learning criteria. In particular, we propose that, for small sets of learning criteria, all pairwise relations should be determined; these relations can then be easily depicted as a map, a diagram detailing the relations. Once we have maps for many relevant sets of learning criteria, the collection of these maps is an Atlas of Computational Learning Theory, informing at a glance about the landscape of computational learning just as a geographical atlas informs about the earth.
In this paper we work toward this goal by providing three example maps, one pertaining to partially set-driven learning, and two pertaining to strongly monotone learning. These maps can serve as blueprints for future maps of similar base structure
Inductive Inference and Reverse Mathematics
The present work investigates inductive inference from the perspective
of reverse mathematics. Reverse mathematics is a framework which relates
the proof strength of theorems and axioms throughout many areas of
mathematics in an interdisciplinary way. The present work looks at
basic notions of learnability including Angluin\u27s tell-tale condition and its variants for learning in the limit and for conservative learning. Furthermore, the more general criterion of partial learning is investigated. These notions are studied in the reverse mathematics context for uniformly and weakly represented families of languages. The results are stated in terms of axioms referring to domination and induction strength