68,697 research outputs found
Pandora's Box Problem with Order Constraints
The Pandora's Box Problem, originally formalized by Weitzman in 1979, models
selection from set of random, alternative options, when evaluation is costly.
This includes, for example, the problem of hiring a skilled worker, where only
one hire can be made, but the evaluation of each candidate is an expensive
procedure. Weitzman showed that the Pandora's Box Problem admits an elegant,
simple solution, where the options are considered in decreasing order of
reservation value,i.e., the value that reduces to zero the expected marginal
gain for opening the box. We study for the first time this problem when order -
or precedence - constraints are imposed between the boxes. We show that,
despite the difficulty of defining reservation values for the boxes which take
into account both in-depth and in-breath exploration of the various options,
greedy optimal strategies exist and can be efficiently computed for tree-like
order constraints. We also prove that finding approximately optimal adaptive
search strategies is NP-hard when certain matroid constraints are used to
further restrict the set of boxes which may be opened, or when the order
constraints are given as reachability constraints on a DAG. We complement the
above result by giving approximate adaptive search strategies based on a
connection between optimal adaptive strategies and non-adaptive strategies with
bounded adaptivity gap for a carefully relaxed version of the problem
Budgeted Reinforcement Learning in Continuous State Space
A Budgeted Markov Decision Process (BMDP) is an extension of a Markov
Decision Process to critical applications requiring safety constraints. It
relies on a notion of risk implemented in the shape of a cost signal
constrained to lie below an - adjustable - threshold. So far, BMDPs could only
be solved in the case of finite state spaces with known dynamics. This work
extends the state-of-the-art to continuous spaces environments and unknown
dynamics. We show that the solution to a BMDP is a fixed point of a novel
Budgeted Bellman Optimality operator. This observation allows us to introduce
natural extensions of Deep Reinforcement Learning algorithms to address
large-scale BMDPs. We validate our approach on two simulated applications:
spoken dialogue and autonomous driving.Comment: N. Carrara and E. Leurent have equally contribute
Feature Engineering for Predictive Modeling using Reinforcement Learning
Feature engineering is a crucial step in the process of predictive modeling.
It involves the transformation of given feature space, typically using
mathematical functions, with the objective of reducing the modeling error for a
given target. However, there is no well-defined basis for performing effective
feature engineering. It involves domain knowledge, intuition, and most of all,
a lengthy process of trial and error. The human attention involved in
overseeing this process significantly influences the cost of model generation.
We present a new framework to automate feature engineering. It is based on
performance driven exploration of a transformation graph, which systematically
and compactly enumerates the space of given options. A highly efficient
exploration strategy is derived through reinforcement learning on past
examples
Efficient Hill Climber for Constrained Pseudo-Boolean Optimization Problems
Efficient hill climbers have been recently proposed for single- and multi-objective pseudo-Boolean optimization problems. For -bounded pseudo-Boolean functions where each variable appears in at most a constant number of subfunctions, it has been theoretically proven that the neighborhood of a solution can be explored in constant time. These hill climbers, combined with a high-level exploration strategy, have shown to improve state of the art methods in experimental studies and open the door to the so-called Gray Box Optimization, where part, but not all, of the details of the objective functions are used to better explore the search space. One important limitation of all the previous proposals is that they can only be applied to unconstrained pseudo-Boolean optimization problems. In this work, we address the constrained case for multi-objective -bounded pseudo-Boolean optimization problems. We find that adding constraints to the pseudo-Boolean problem has a linear computational cost in the hill climber.Universidad de Málaga. Campus de Excelencia Internacional AndalucĂa Tech
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