11 research outputs found
Think Eternally: Improved Algorithms for the Temp Secretary Problem and Extensions
The Temp Secretary Problem was recently introduced by [Fiat et al., ESA 2015]. It is a generalization of the Secretary Problem, in which commitments are temporary for a fixed duration. We present a simple online algorithm with improved performance guarantees for cases already considered by [Fiat et al., ESA 2015] and give competitive ratios for new generalizations of the problem. In the classical setting, where candidates have identical contract durations gamma << 1 and we are allowed to hire up to B candidates simultaneously, our algorithm is (1/2) - O(sqrt{gamma})-competitive. For large B, the bound improves to 1 - O(1/sqrt{B}) - O(sqrt{gamma}).
Furthermore we generalize the problem from cardinality constraints towards general packing constraints. We achieve a competitive ratio of 1 - O(sqrt{(1+log(d) + log(B))/B}) - O(sqrt{gamma}), where d is the sparsity of the constraint matrix and B is generalized to the capacity ratio of linear constraints. Additionally we extend the problem towards arbitrary hiring durations.
Our algorithmic approach is a relaxation that aggregates all temporal constraints into a non-temporal constraint. Then we apply a linear scaling algorithm that, on every arrival, computes a tentative solution on the input that is known up to this point. This tentative solution uses the non-temporal, relaxed constraints scaled down linearly by the amount of time that has already passed
Think Eternally: Improved Algorithms for the Temp Secretary Problem and Extensions
The Temp Secretary Problem was recently introduced by [Fiat et al., ESA 2015]. It is a generalization of the Secretary Problem, in which commitments are temporary for a fixed duration. We present a simple online algorithm with improved performance guarantees for cases already considered by [Fiat et al., ESA 2015] and give competitive ratios for new generalizations of the problem. In the classical setting, where candidates have identical contract durations gamma << 1 and we are allowed to hire up to B candidates simultaneously, our algorithm is (1/2) - O(sqrt{gamma})-competitive. For large B, the bound improves to 1 - O(1/sqrt{B}) - O(sqrt{gamma}).
Furthermore we generalize the problem from cardinality constraints towards general packing constraints. We achieve a competitive ratio of 1 - O(sqrt{(1+log(d) + log(B))/B}) - O(sqrt{gamma}), where d is the sparsity of the constraint matrix and B is generalized to the capacity ratio of linear constraints. Additionally we extend the problem towards arbitrary hiring durations.
Our algorithmic approach is a relaxation that aggregates all temporal constraints into a non-temporal constraint. Then we apply a linear scaling algorithm that, on every arrival, computes a tentative solution on the input that is known up to this point. This tentative solution uses the non-temporal, relaxed constraints scaled down linearly by the amount of time that has already passed
Constrained Online Two-stage Stochastic Optimization: Algorithm with (and without) Predictions
We consider an online two-stage stochastic optimization with long-term
constraints over a finite horizon of periods. At each period, we take the
first-stage action, observe a model parameter realization and then take the
second-stage action from a feasible set that depends both on the first-stage
decision and the model parameter. We aim to minimize the cumulative objective
value while guaranteeing that the long-term average second-stage decision
belongs to a set. We develop online algorithms for the online two-stage problem
from adversarial learning algorithms. Also, the regret bound of our algorithm
can be reduced to the regret bound of embedded adversarial learning algorithms.
Based on this framework, we obtain new results under various settings. When the
model parameters are drawn from unknown non-stationary distributions and we are
given machine-learned predictions of the distributions, we develop a new
algorithm from our framework with a regret , where
measures the total inaccuracy of the machine-learned predictions. We then
develop another algorithm that works when no machine-learned predictions are
given and show the performances.Comment: arXiv admin note: substantial text overlap with arXiv:2302.0099
A Field Guide for Pacing Budget and ROS Constraints
Budget pacing is a popular service that has been offered by major internet
advertising platforms since their inception. Budget pacing systems seek to
optimize advertiser returns subject to budget constraints by smoothly spending
advertiser budgets. In the past few years, autobidding products that provide
real-time bidding as a service to advertisers have seen a prominent rise in
adoption. A popular autobidding strategy is value maximization subject to
return-on-spend (ROS) constraints. For historical/business reasons, the systems
that govern these two services, namely budget pacing and ROS pacing, are not
always a unified and coordinated entity that optimizes a global objective
subject to both constraints. The purpose of this work is to theoretically and
empirically compare algorithms with different degrees of coordination between
these two pacing systems.
In particular, we compare (a) a fully-decoupled sequential algorithm that
first constructs the advertiser's ROS-pacing bid and then lowers that bid for
budget pacing; (b) a minimally-coupled min-pacing algorithm that runs these two
services independently, obtains the bid multipliers from both of them and
applies the minimum of the two multipliers as the effective multiplier; and (c)
a fully-coupled dual-based algorithm that optimally combines the dual variables
from both the systems. Our main contribution is to theoretically analyze the
min-pacing algorithm and show that it attains similar guarantees to the
fully-coupled canonical dual-based algorithm. On the other hand, we show that
the sequential algorithm, even though appealing by virtue of being fully
decoupled, could badly violate the constraints. We validate our theoretical
findings empirically by showing that the min-pacing algorithm performs almost
as well as the canonical dual-based algorithm on a semi-synthetic dataset based
on a large online advertising platform's data
Degeneracy is OK: Logarithmic Regret for Network Revenue Management with Indiscrete Distributions
We study the classical Network Revenue Management (NRM) problem with
accept/reject decisions and IID arrivals. We consider a distributional form
where each arrival must fall under a finite number of possible categories, each
with a deterministic resource consumption vector, but a random value
distributed continuously over an interval. We develop an online algorithm that
achieves regret under this model, with the only (necessary)
assumption being that the probability densities are bounded away from 0. We
derive a second result that achieves regret under an additional
assumption of second-order growth. To our knowledge, these are the first
results achieving logarithmic-level regret in an NRM model with continuous
values that do not require any kind of ``non-degeneracy'' assumptions. Our
results are achieved via new techniques including a new method of bounding
myopic regret, a ``semi-fluid'' relaxation of the offline allocation, and an
improved bound on the ``dual convergence''