16 research outputs found
Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learning
Many real-world optimization problems contain unknown parameters that must be
predicted prior to solving. To train the predictive machine learning (ML)
models involved, the commonly adopted approach focuses on maximizing predictive
accuracy. However, this approach does not always lead to the minimization of
the downstream task loss. Decision-focused learning (DFL) is a recently
proposed paradigm whose goal is to train the ML model by directly minimizing
the task loss. However, state-of-the-art DFL methods are limited by the
assumptions they make about the structure of the optimization problem (e.g.,
that the problem is linear) and by the fact that can only predict parameters
that appear in the objective function. In this work, we address these
limitations by instead predicting \textit{distributions} over parameters and
adopting score function gradient estimation (SFGE) to compute decision-focused
updates to the predictive model, thereby widening the applicability of DFL. Our
experiments show that by using SFGE we can: (1) deal with predictions that
occur both in the objective function and in the constraints; and (2)
effectively tackle two-stage stochastic optimization problems
Planar Matching in Streams Revisited
We present data stream algorithms for estimating the size or weight of the maximum matching in low arboricity graphs. A large body of work has focused on improving the constant approximation factor for general graphs when the data stream algorithm is permitted O(n polylog n) space where n is the number of nodes. This space is necessary if the algorithm must return the matching. Recently, Esfandiari et al. (SODA 2015) showed that it was possible to estimate the maximum cardinality of a matching in a planar graph up to a factor of 24+epsilon using O(epsilon^{-2} n^{2/3} polylog n) space. We first present an algorithm (with a simple analysis) that improves this to a factor 5+epsilon using the same space. We also improve upon the previous results for other graphs with bounded arboricity. We then present a factor 12.5 approximation for matching in planar graphs that can be implemented using O(log n) space in the adjacency list data stream model where the stream is a concatenation of the adjacency lists of the graph. The main idea behind our results is finding "local" fractional matchings, i.e., fractional matchings where the value of any edge e is solely determined by the edges sharing an endpoint with e. Our work also improves upon the results for the dynamic data stream model where the stream consists of a sequence of edges being inserted and deleted from the graph. We also extend our results to weighted graphs, improving over the bounds given by Bury and Schwiegelshohn (ESA 2015), via a reduction to the unweighted problem that increases the approximation by at most a factor of two
Online graph coloring against a randomized adversary
Electronic version of an article published as
Online graph coloring against a randomized adversary. "International journal of foundations of computer science", 1 Juny 2018, vol. 29, núm. 4, p. 551-569. DOI:10.1142/S0129054118410058 © 2018 copyright World Scientific Publishing Company. https://www.worldscientific.com/doi/abs/10.1142/S0129054118410058We consider an online model where an adversary constructs a set of 2s instances S instead of one single instance. The algorithm knows S and the adversary will choose one instance from S at random to present to the algorithm. We further focus on adversaries that construct sets of k-chromatic instances. In this setting, we provide upper and lower bounds on the competitive ratio for the online graph coloring problem as a function of the parameters in this model. Both bounds are linear in s and matching upper and lower bound are given for a specific set of algorithms that we call “minimalistic online algorithms”.Peer ReviewedPostprint (author's final draft
A 2-Approximation Algorithm for the Complementary Maximal Strip Recovery Problem
The Maximal Strip Recovery problem (MSR) and its complementary (CMSR) are well-studied NP-hard problems in computational genomics. The input of these dual problems are two signed permutations. The goal is to delete some gene markers from both permutations, such that, in the remaining permutations, each gene marker has at least one common neighbor. Equivalently, the resulting permutations could be partitioned into common strips of length at least two. Then MSR is to maximize the number of remaining genes, while the objective of CMSR is to delete the minimum number of gene markers. In this paper, we present a new approximation algorithm for the Complementary Maximal Strip Recovery (CMSR) problem. Our approximation factor is 2, improving the currently best 7/3-approximation algorithm. Although the improvement on the factor is not huge, the analysis is greatly simplified by a compensating method, commonly referred to as the non-oblivious local search technique. In such a method a substitution may not always increase the value of the current solution (it sometimes may even decrease the solution value), though it always improves the value of another function seemingly unrelated to the objective function
Tropically convex constraint satisfaction
A semilinear relation S is max-closed if it is preserved by taking the
componentwise maximum. The constraint satisfaction problem for max-closed
semilinear constraints is at least as hard as determining the winner in Mean
Payoff Games, a notorious problem of open computational complexity. Mean Payoff
Games are known to be in the intersection of NP and co-NP, which is not known
for max-closed semilinear constraints. Semilinear relations that are max-closed
and additionally closed under translations have been called tropically convex
in the literature. One of our main results is a new duality for open tropically
convex relations, which puts the CSP for tropically convex semilinaer
constraints in general into NP intersected co-NP. This extends the
corresponding complexity result for scheduling under and-or precedence
constraints, or equivalently the max-atoms problem. To this end, we present a
characterization of max-closed semilinear relations in terms of syntactically
restricted first-order logic, and another characterization in terms of a finite
set of relations L that allow primitive positive definitions of all other
relations in the class. We also present a subclass of max-closed constraints
where the CSP is in P; this class generalizes the class of max-closed
constraints over finite domains, and the feasibility problem for max-closed
linear inequalities. Finally, we show that the class of max-closed semilinear
constraints is maximal in the sense that as soon as a single relation that is
not max-closed is added to L, the CSP becomes NP-hard.Comment: 29 pages, 2 figure
Constraint Satisfaction Problems over Numeric Domains
We present a survey of complexity results for constraint satisfaction problems (CSPs) over the integers, the rationals, the reals, and the complex numbers. Examples of such problems are feasibility of linear programs, integer linear programming, the max-atoms problem, Hilbert\u27s tenth problem, and many more. Our particular focus is to identify those CSPs that can be solved in polynomial time, and to distinguish them from CSPs that are NP-hard. A very helpful tool for obtaining complexity classifications in this context is the concept of a polymorphism from universal algebra
Online Conversion with Switching Costs: Robust and Learning-Augmented Algorithms
We introduce and study online conversion with switching costs, a family of
online problems that capture emerging problems at the intersection of energy
and sustainability. In this problem, an online player attempts to purchase
(alternatively, sell) fractional shares of an asset during a fixed time horizon
with length . At each time step, a cost function (alternatively, price
function) is revealed, and the player must irrevocably decide an amount of
asset to convert. The player also incurs a switching cost whenever their
decision changes in consecutive time steps, i.e., when they increase or
decrease their purchasing amount. We introduce competitive (robust)
threshold-based algorithms for both the minimization and maximization variants
of this problem, and show they are optimal among deterministic online
algorithms. We then propose learning-augmented algorithms that take advantage
of untrusted black-box advice (such as predictions from a machine learning
model) to achieve significantly better average-case performance without
sacrificing worst-case competitive guarantees. Finally, we empirically evaluate
our proposed algorithms using a carbon-aware EV charging case study, showing
that our algorithms substantially improve on baseline methods for this problem.Comment: Accepted to SIGMETRICS / Performance '24. 47 pages, 9 figure