Learning Max-CSPs via Active Constraint Acquisition

Constraint acquisition can assist non-expert users to model their problems as constraint networks. In active constraint acquisition, this is achieved through an interaction between the learner, who posts examples, and the user who classifies them as solutions or not. Although there has been recent progress in active constraint acquisition, the focus has only been on learning satisfaction problems with hard constraints. In this paper, we deal with the problem of learning soft constraints in optimization problems via active constraint acquisition, specifically in the context of the Max-CSP. Towards this, we first introduce a new type of queries in the context of constraint acquisition, namely partial preference queries, and then we present a novel algorithm for learning soft constraints in Max-CSPs, using such queries. We also give some experimental results

Learning From Biased Soft Labels

Knowledge distillation has been widely adopted in a variety of tasks and has achieved remarkable successes. Since its inception, many researchers have been intrigued by the dark knowledge hidden in the outputs of the teacher model. Recently, a study has demonstrated that knowledge distillation and label smoothing can be unified as learning from soft labels. Consequently, how to measure the effectiveness of the soft labels becomes an important question. Most existing theories have stringent constraints on the teacher model or data distribution, and many assumptions imply that the soft labels are close to the ground-truth labels. This paper studies whether biased soft labels are still effective. We present two more comprehensive indicators to measure the effectiveness of such soft labels. Based on the two indicators, we give sufficient conditions to ensure biased soft label based learners are classifier-consistent and ERM learnable. The theory is applied to three weakly-supervised frameworks. Experimental results validate that biased soft labels can also teach good students, which corroborates the soundness of the theory

Constraint-based Temporal Reasoning with Preferences

Often we need to work in scenarios where events happen over time and preferences are associated to event distances and durations. Soft temporal constraints allow one to describe in a natural way problems arising in such scenarios. In general, solving soft temporal problems require exponential time in the worst case, but there are interesting subclasses of problems which are polynomially solvable. In this paper we identify one of such subclasses giving tractability results. Moreover, we describe two solvers for this class of soft temporal problems, and we show some experimental results. The random generator used to build the problems on which tests are performed is also described. We also compare the two solvers highlighting the tradeoff between performance and robustness. Sometimes, however, temporal local preferences are difficult to set, and it may be easier instead to associate preferences to some complete solutions of the problem. To model everything in a uniform way via local preferences only, and also to take advantage of the existing constraint solvers which exploit only local preferences, we show that machine learning techniques can be useful in this respect. In particular, we present a learning module based on a gradient descent technique which induces local temporal preferences from global ones. We also show the behavior of the learning module on randomly-generated examples

On Tackling the Limits of Resolution in SAT Solving

The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for formulas in conjunctive normal form (CNF) to the problem of solving maximum satisfiability over Horn formulas. Given the new transformation, the paper proves a polynomial bound on the number of MaxSAT resolution steps for pigeonhole formulas. This result is in clear contrast with earlier results on the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper also establishes the same polynomial bound in the case of modern core-guided MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard for CDCL SAT solvers, show that these can be efficiently solved with modern MaxSAT solvers