218 research outputs found
Logical Reduction of Metarules
International audienceMany forms of inductive logic programming (ILP) use metarules, second-order Horn clauses, to define the structure of learnable programs and thus the hypothesis space. Deciding which metarules to use for a given learning task is a major open problem and is a trade-off between efficiency and expressivity: the hypothesis space grows given more metarules, so we wish to use fewer metarules, but if we use too few metarules then we lose expressivity. In this paper, we study whether fragments of metarules can be logically reduced to minimal finite subsets. We consider two traditional forms of logical reduction: subsumption and entailment. We also consider a new reduction technique called derivation reduction, which is based on SLD-resolution. We compute reduced sets of metarules for fragments relevant to ILP and theoretically show whether these reduced sets are reductions for more general infinite fragments. We experimentally compare learning with reduced sets of metarules on three domains: Michalski trains, string transformations, and game rules. In general, derivation reduced sets of metarules outperform subsumption and entailment reduced sets, both in terms of predictive accuracies and learning times
Recent Advances in Fully Dynamic Graph Algorithms
In recent years, significant advances have been made in the design and
analysis of fully dynamic algorithms. However, these theoretical results have
received very little attention from the practical perspective. Few of the
algorithms are implemented and tested on real datasets, and their practical
potential is far from understood. Here, we present a quick reference guide to
recent engineering and theory results in the area of fully dynamic graph
algorithms
Thompson Sampling Regret Bounds for Contextual Bandits with sub-Gaussian rewards
In this work, we study the performance of the Thompson Sampling algorithm for
Contextual Bandit problems based on the framework introduced by Neu et al. and
their concept of lifted information ratio. First, we prove a comprehensive
bound on the Thompson Sampling expected cumulative regret that depends on the
mutual information of the environment parameters and the history. Then, we
introduce new bounds on the lifted information ratio that hold for sub-Gaussian
rewards, thus generalizing the results from Neu et al. which analysis requires
binary rewards. Finally, we provide explicit regret bounds for the special
cases of unstructured bounded contextual bandits, structured bounded contextual
bandits with Laplace likelihood, structured Bernoulli bandits, and bounded
linear contextual bandits.Comment: 8 pages: 5 of the main text, 1 of references, and 2 of appendices.
Accepted to ISIT 202
On the Minimax Regret in Online Ranking with Top-k Feedback
In online ranking, a learning algorithm sequentially ranks a set of items and
receives feedback on its ranking in the form of relevance scores. Since
obtaining relevance scores typically involves human annotation, it is of great
interest to consider a partial feedback setting where feedback is restricted to
the top- items in the rankings. Chaudhuri and Tewari [2017] developed a
framework to analyze online ranking algorithms with top feedback. A key
element in their work was the use of techniques from partial monitoring. In
this paper, we further investigate online ranking with top feedback and
solve some open problems posed by Chaudhuri and Tewari [2017]. We provide a
full characterization of minimax regret rates with the top feedback model
for all and for the following ranking performance measures: Pairwise Loss,
Discounted Cumulative Gain, and Precision@n. In addition, we give an efficient
algorithm that achieves the minimax regret rate for Precision@n
CRIMED: Lower and Upper Bounds on Regret for Bandits with Unbounded Stochastic Corruption
We investigate the regret-minimisation problem in a multi-armed bandit
setting with arbitrary corruptions. Similar to the classical setup, the agent
receives rewards generated independently from the distribution of the arm
chosen at each time. However, these rewards are not directly observed. Instead,
with a fixed , the agent observes a sample from
the chosen arm's distribution with probability , or from an
arbitrary corruption distribution with probability . Importantly,
we impose no assumptions on these corruption distributions, which can be
unbounded. In this setting, accommodating potentially unbounded corruptions, we
establish a problem-dependent lower bound on regret for a given family of arm
distributions. We introduce CRIMED, an asymptotically-optimal algorithm that
achieves the exact lower bound on regret for bandits with Gaussian
distributions with known variance. Additionally, we provide a finite-sample
analysis of CRIMED's regret performance. Notably, CRIMED can effectively handle
corruptions with values as high as . Furthermore, we
develop a tight concentration result for medians in the presence of arbitrary
corruptions, even with values up to , which may be
of independent interest. We also discuss an extension of the algorithm for
handling misspecification in Gaussian model.Comment: 50 pages; 4 figure
Second-Order Finite Automata
Traditionally, finite automata theory has been used as a framework for the representation of possibly infinite sets of strings. In this work, we introduce the notion of second-order finite automata, a formalism that combines finite automata with ordered decision diagrams, with the aim of representing possibly infinite sets of sets of strings. Our main result states that second-order finite automata can be canonized with respect to the second-order languages they represent. Using this canonization result, we show that sets of sets of strings represented by second-order finite automata are closed under the usual Boolean operations, such as union, intersection, difference and even under a suitable notion of complementation. Additionally, emptiness of intersection and inclusion are decidable. We provide two algorithmic applications for second-order automata. First, we show that several width/size minimization problems for deterministic and nondeterministic ODDs are solvable in fixed-parameter tractable time when parameterized by the width of the input ODD. In particular, our results imply FPT algorithms for corresponding width/size minimization problems for ordered binary decision diagrams (OBDDs) with a fixed variable ordering. Previously, only algorithms that take exponential time in the size of the input OBDD were known for width minimization, even for OBDDs of constant width. Second, we show that for each k and w one can count the number of distinct functions computable by ODDs of width at most w and length k in time h(|Σ|,w) ⋅ kO(1), for a suitable . This improves exponentially on the time necessary to explicitly enumerate all such functions, which is exponential in both the width parameter w and in the length k of the ODDs.publishedVersio
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