3,648 research outputs found
Social welfare and profit maximization from revealed preferences
Consider the seller's problem of finding optimal prices for her
(divisible) goods when faced with a set of consumers, given that she can
only observe their purchased bundles at posted prices, i.e., revealed
preferences. We study both social welfare and profit maximization with revealed
preferences. Although social welfare maximization is a seemingly non-convex
optimization problem in prices, we show that (i) it can be reduced to a dual
convex optimization problem in prices, and (ii) the revealed preferences can be
interpreted as supergradients of the concave conjugate of valuation, with which
subgradients of the dual function can be computed. We thereby obtain a simple
subgradient-based algorithm for strongly concave valuations and convex cost,
with query complexity , where is the additive
difference between the social welfare induced by our algorithm and the optimum
social welfare. We also study social welfare maximization under the online
setting, specifically the random permutation model, where consumers arrive
one-by-one in a random order. For the case where consumer valuations can be
arbitrary continuous functions, we propose a price posting mechanism that
achieves an expected social welfare up to an additive factor of
from the maximum social welfare. Finally, for profit maximization (which may be
non-convex in simple cases), we give nearly matching upper and lower bounds on
the query complexity for separable valuations and cost (i.e., each good can be
treated independently)
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The Variable Markov Oracle: Algorithms for Human Gesture Applications
This article introduces the Variable Markov Oracle (VMO) data structure for multivariate time series indexing. VMO can identify repetitive fragments and find sequential similarities between observations. VMO can also be viewed as a combination of online clustering algorithms with variable-order Markov constraints. The authors use VMO for gesture query-by-content and gesture following. A probabilistic interpretation of the VMO query-matching algorithm is proposed to find an analogy to the inference problem in a hidden Markov model (HMM). This probabilistic interpretation extends VMO to be not only a data structure but also a model for time series. Query-by-content experiments were conducted on a gesture database that was recorded using a Kinect 3D camera, showing state-of-the-art performance. The query-by-content experiments' results are compared to previous works using HMM and dynamic time warping. Gesture following is described in the context of an interactive dance environment that aims to integrate human movements with computer-generated graphics to create an augmented reality performance
Allocation Problems in Ride-Sharing Platforms: Online Matching with Offline Reusable Resources
Bipartite matching markets pair agents on one side of a market with agents,
items, or contracts on the opposing side. Prior work addresses online bipartite
matching markets, where agents arrive over time and are dynamically matched to
a known set of disposable resources. In this paper, we propose a new model,
Online Matching with (offline) Reusable Resources under Known Adversarial
Distributions (OM-RR-KAD), in which resources on the offline side are reusable
instead of disposable; that is, once matched, resources become available again
at some point in the future. We show that our model is tractable by presenting
an LP-based adaptive algorithm that achieves an online competitive ratio of 1/2
- eps for any given eps greater than 0. We also show that no non-adaptive
algorithm can achieve a ratio of 1/2 + o(1) based on the same benchmark LP.
Through a data-driven analysis on a massive openly-available dataset, we show
our model is robust enough to capture the application of taxi dispatching
services and ride-sharing systems. We also present heuristics that perform well
in practice.Comment: To appear in AAAI 201
How the Experts Algorithm Can Help Solve LPs Online
We consider the problem of solving packing/covering LPs online, when the
columns of the constraint matrix are presented in random order. This problem
has received much attention and the main focus is to figure out how large the
right-hand sides of the LPs have to be (compared to the entries on the
left-hand side of the constraints) to allow -approximations
online. It is known that the right-hand sides have to be times the left-hand sides, where is the number of constraints.
In this paper we give a primal-dual algorithm that achieve this bound for
mixed packing/covering LPs. Our algorithms construct dual solutions using a
regret-minimizing online learning algorithm in a black-box fashion, and use
them to construct primal solutions. The adversarial guarantee that holds for
the constructed duals helps us to take care of most of the correlations that
arise in the algorithm; the remaining correlations are handled via martingale
concentration and maximal inequalities. These ideas lead to conceptually simple
and modular algorithms, which we hope will be useful in other contexts.Comment: An extended abstract appears in the 22nd European Symposium on
Algorithms (ESA 2014
The Social Medium Selection Game
We consider in this paper competition of content creators in routing their
content through various media. The routing decisions may correspond to the
selection of a social network (e.g. twitter versus facebook or linkedin) or of
a group within a given social network. The utility for a player to send its
content to some medium is given as the difference between the dissemination
utility at this medium and some transmission cost. We model this game as a
congestion game and compute the pure potential of the game. In contrast to the
continuous case, we show that there may be various equilibria. We show that the
potential is M-concave which allows us to characterize the equilibria and to
propose an algorithm for computing it. We then give a learning mechanism which
allow us to give an efficient algorithm to determine an equilibrium. We finally
determine the asymptotic form of the equilibrium and discuss the implications
on the social medium selection problem
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