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Bounding the Suboptimality of Reusing Subproblems
, 1998
"... We are interested in the problem of determining a course of action to achieve a desired objective in a nondeterministic environment. Markov decision processes (MDPs) provide a framework for representing this action selection problem, and there are a number of algorithms that learn optimal policies w ..."
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Cited by 13 (5 self)
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to subproblems. This is done within a restricted class of MDPs, namely those where nonzero reward is received only upon reaching a goal state. We introduce the definition of a subproblem within this class and provide motivation for how reuse of subproblem solutions can speed up learning. The contribution
Subproblems and NPCompleteness Theory ∗
"... Subproblems have become an important object of NPcompleteness theory since its beginning. In this paper, we show some undesirable consequences for subproblems deduced by the standard foundation of the theory, which are different from the practical viewpoint of computation. By the consequences, we c ..."
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Subproblems have become an important object of NPcompleteness theory since its beginning. In this paper, we show some undesirable consequences for subproblems deduced by the standard foundation of the theory, which are different from the practical viewpoint of computation. By the consequences, we
Optimality Conditions for CDT Subproblem
, 1997
"... : In this paper, we give necessary and sufficient optimality conditions which are easy verified for the local solution of CelisDennisTapia subproblem (CDT subproblem) where the Hessian at this local solution has one negative eigenvalue. If CDT subproblem has no global solution with Hessian of Lagr ..."
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Cited by 1 (0 self)
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: In this paper, we give necessary and sufficient optimality conditions which are easy verified for the local solution of CelisDennisTapia subproblem (CDT subproblem) where the Hessian at this local solution has one negative eigenvalue. If CDT subproblem has no global solution with Hessian
Machine Learning for Subproblem Selection
 In Proceedings 17th International Conf. on Machine Learning
, 2000
"... Subproblem generation, solution, and recombination is a standard approach to combinatorial optimization problems. In many settings identifying suitable subproblems is itself a significant component of the technique. Such subproblems are often identified using a heuristic rule. Here we show how ..."
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Cited by 4 (0 self)
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Subproblem generation, solution, and recombination is a standard approach to combinatorial optimization problems. In many settings identifying suitable subproblems is itself a significant component of the technique. Such subproblems are often identified using a heuristic rule. Here we show
The generalized trust region subproblem
, 2012
"... The interval bounded generalized trust region subproblem (GTRS) consists in minimizing a general quadratic objective, q0(x) → min, subject to an upper and lower bounded general quadratic constraint, ℓ ≤ q1(x) ≤ u. This means that there are no definiteness assumptions on either quadratic function. ..."
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Cited by 2 (0 self)
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The interval bounded generalized trust region subproblem (GTRS) consists in minimizing a general quadratic objective, q0(x) → min, subject to an upper and lower bounded general quadratic constraint, ℓ ≤ q1(x) ≤ u. This means that there are no definiteness assumptions on either quadratic function
Bounding the Suboptimality of Reusing Subproblems
, 1998
"... We are interested in the problem of determining a course of action to achieve a desired objective in a nondeterministic environment. Markov decision processes (MDPs) provide a framework for representing this action selection problem, and there are a number of algorithms that learn optimal poli ..."
Abstract
 Add to MetaCart
that are solutions to subproblems. This is done within a restricted class of MDPs, namely those where nonzero reward is received only upon reaching a goal state. We introduce the definition of a subproblem within this class and provide motivation for how reuse of subproblem solutions can speed up learning
Detecting and Exploiting Subproblem Tractability
"... Constraint satisfaction problems may be nearly tractable. For instance, most of the relations in a problem might belong to a tractable language. We introduce a method to take advantage of this fact by computing a backdoor to this tractable language. The method can be applied to many tractable classe ..."
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Cited by 2 (1 self)
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Constraint satisfaction problems may be nearly tractable. For instance, most of the relations in a problem might belong to a tractable language. We introduce a method to take advantage of this fact by computing a backdoor to this tractable language. The method can be applied to many tractable classes for which the membership test is itself tractable. We introduce therefore two polynomial membership testing algorithms, to check if a language is closed under a majority or conservative Mal’tsev polymorphism, respectively. Then we show that computing a minimal backdoor for such classes is fixed parameter tractable (FPT) if the tractable subset of relations is given, and W[2]complete otherwise. Finally, we report experimental results on the XCSP benchmark set. We identified a few promising problem classes where problems were nearly closed under a majority polymorphism and small backdoors could be computed.
The generalized trust region subproblem
, 2012
"... The interval bounded generalized trust region subproblem (GTRS) consists in minimizing a general quadratic objective, q0(x) → min, subject to an upper and lower bounded general quadratic constraint, ℓ ≤ q1(x) ≤ u. This means that there are no definiteness assumptions on either quadratic function. ..."
Abstract
 Add to MetaCart
The interval bounded generalized trust region subproblem (GTRS) consists in minimizing a general quadratic objective, q0(x) → min, subject to an upper and lower bounded general quadratic constraint, ℓ ≤ q1(x) ≤ u. This means that there are no definiteness assumptions on either quadratic function
Results 1  10
of
50,964