35 research outputs found
Metric embeddings with relaxed guarantees
We consider the problem of embedding finite metrics with slack: We seek to produce embeddings with small dimension and distortion while allowing a (small) constant fraction of all distances to be arbitrarily distorted. This definition is motivated by recent research in the networking community, which achieved striking empirical success at embedding Internet latencies with low distortion into low-dimensional Euclidean space, provided that some small slack is allowed. Answering an open question of Kleinberg, Slivkins, and Wexler [in Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, 2004], we show that provable guarantees of this type can in fact be achieved in general: Any finite metric space can be embedded, with constant slack and constant distortion, into constant-dimensional Euclidean space. We then show that there exist stronger embeddings into l 1 which exhibit gracefully degrading distortion: There is a single embedding into l 1 that achieves distortion at most O (log 1/∈) on all but at most an ∈ fraction of distances simultaneously for all ∈ > 0. We extend this with distortion O (log 1/∈) 1/p to maps into general l p, p ≥ 1, for several classes of metrics, including those with bounded doubling dimension and those arising from the shortest-path metric of a graph with an excluded minor. Finally, we show that many of our constructions are tight and give a general technique to obtain lower bounds for ∈-slack embeddings from lower bounds for low-distortion embeddings. © 2009 Society for Industrial and Applied Mathematics.published_or_final_versio
Incentivizing Exploration with Heterogeneous Value of Money
Recently, Frazier et al. proposed a natural model for crowdsourced
exploration of different a priori unknown options: a principal is interested in
the long-term welfare of a population of agents who arrive one by one in a
multi-armed bandit setting. However, each agent is myopic, so in order to
incentivize him to explore options with better long-term prospects, the
principal must offer the agent money. Frazier et al. showed that a simple class
of policies called time-expanded are optimal in the worst case, and
characterized their budget-reward tradeoff.
The previous work assumed that all agents are equally and uniformly
susceptible to financial incentives. In reality, agents may have different
utility for money. We therefore extend the model of Frazier et al. to allow
agents that have heterogeneous and non-linear utilities for money. The
principal is informed of the agent's tradeoff via a signal that could be more
or less informative.
Our main result is to show that a convex program can be used to derive a
signal-dependent time-expanded policy which achieves the best possible
Lagrangian reward in the worst case. The worst-case guarantee is matched by
so-called "Diamonds in the Rough" instances; the proof that the guarantees
match is based on showing that two different convex programs have the same
optimal solution for these specific instances. These results also extend to the
budgeted case as in Frazier et al. We also show that the optimal policy is
monotone with respect to information, i.e., the approximation ratio of the
optimal policy improves as the signals become more informative.Comment: WINE 201
Navigability is a Robust Property
The Small World phenomenon has inspired researchers across a number of
fields. A breakthrough in its understanding was made by Kleinberg who
introduced Rank Based Augmentation (RBA): add to each vertex independently an
arc to a random destination selected from a carefully crafted probability
distribution. Kleinberg proved that RBA makes many networks navigable, i.e., it
allows greedy routing to successfully deliver messages between any two vertices
in a polylogarithmic number of steps. We prove that navigability is an inherent
property of many random networks, arising without coordination, or even
independence assumptions
Discovering Valuable Items from Massive Data
Suppose there is a large collection of items, each with an associated cost
and an inherent utility that is revealed only once we commit to selecting it.
Given a budget on the cumulative cost of the selected items, how can we pick a
subset of maximal value? This task generalizes several important problems such
as multi-arm bandits, active search and the knapsack problem. We present an
algorithm, GP-Select, which utilizes prior knowledge about similarity be- tween
items, expressed as a kernel function. GP-Select uses Gaussian process
prediction to balance exploration (estimating the unknown value of items) and
exploitation (selecting items of high value). We extend GP-Select to be able to
discover sets that simultaneously have high utility and are diverse. Our
preference for diversity can be specified as an arbitrary monotone submodular
function that quantifies the diminishing returns obtained when selecting
similar items. Furthermore, we exploit the structure of the model updates to
achieve an order of magnitude (up to 40X) speedup in our experiments without
resorting to approximations. We provide strong guarantees on the performance of
GP-Select and apply it to three real-world case studies of industrial
relevance: (1) Refreshing a repository of prices in a Global Distribution
System for the travel industry, (2) Identifying diverse, binding-affine
peptides in a vaccine de- sign task and (3) Maximizing clicks in a web-scale
recommender system by recommending items to users
Linear-Space Approximate Distance Oracles for Planar, Bounded-Genus, and Minor-Free Graphs
A (1 + eps)-approximate distance oracle for a graph is a data structure that
supports approximate point-to-point shortest-path-distance queries. The most
relevant measures for a distance-oracle construction are: space, query time,
and preprocessing time. There are strong distance-oracle constructions known
for planar graphs (Thorup, JACM'04) and, subsequently, minor-excluded graphs
(Abraham and Gavoille, PODC'06). However, these require Omega(eps^{-1} n lg n)
space for n-node graphs. We argue that a very low space requirement is
essential. Since modern computer architectures involve hierarchical memory
(caches, primary memory, secondary memory), a high memory requirement in effect
may greatly increase the actual running time. Moreover, we would like data
structures that can be deployed on small mobile devices, such as handhelds,
which have relatively small primary memory. In this paper, for planar graphs,
bounded-genus graphs, and minor-excluded graphs we give distance-oracle
constructions that require only O(n) space. The big O hides only a fixed
constant, independent of \epsilon and independent of genus or size of an
excluded minor. The preprocessing times for our distance oracle are also faster
than those for the previously known constructions. For planar graphs, the
preprocessing time is O(n lg^2 n). However, our constructions have slower query
times. For planar graphs, the query time is O(eps^{-2} lg^2 n). For our
linear-space results, we can in fact ensure, for any delta > 0, that the space
required is only 1 + delta times the space required just to represent the graph
itself
Parameterized Directed -Chinese Postman Problem and Arc-Disjoint Cycles Problem on Euler Digraphs
In the Directed -Chinese Postman Problem (-DCPP), we are given a
connected weighted digraph and asked to find non-empty closed directed
walks covering all arcs of such that the total weight of the walks is
minimum. Gutin, Muciaccia and Yeo (Theor. Comput. Sci. 513 (2013) 124--128)
asked for the parameterized complexity of -DCPP when is the parameter.
We prove that the -DCPP is fixed-parameter tractable.
We also consider a related problem of finding arc-disjoint directed
cycles in an Euler digraph, parameterized by . Slivkins (ESA 2003) showed
that this problem is W[1]-hard for general digraphs. Generalizing another
result by Slivkins, we prove that the problem is fixed-parameter tractable for
Euler digraphs. The corresponding problem on vertex-disjoint cycles in Euler
digraphs remains W[1]-hard even for Euler digraphs
A budget feasible peer graded mechanism for iot-based crowdsourcing
We develop and extend a line of recent works on the design of mechanisms for heterogeneous tasks assignment problem in ’crowdsourcing’. The budgeted market we consider consists of multiple task requesters and multiple IoT devices as task executers. In this, each task requester is endowed with a single distinct task along with the publicly known budget. Also, each IoT device has valuations as the cost for executing the tasks and quality, which are private. Given such scenario, the objective is to select a subset of IoT devices for each task, such that the total payment made is within the allotted quota of the budget while attaining a threshold quality. For the purpose of determining the unknown quality of the IoT devices we have utilized the concept of peer grading. In this paper, we have carefully crafted a truthful budget feasible mechanism for the problem under investigation that also allows us to have the true information about the quality of the IoT devices. Further, we have extended the set-up considering the case where the tasks are divisible in nature and the IoT devices are working collaboratively, instead of, a single entity for executing each task. We have designed the budget feasible mechanisms for the extended versions. The simulations are performed in order to measure the efficacy of our proposed mechanismPeer ReviewedPostprint (author's final draft
Bayesian Policy Reuse
A long-lived autonomous agent should be able to respond online to novel
instances of tasks from a familiar domain. Acting online requires 'fast'
responses, in terms of rapid convergence, especially when the task instance has
a short duration, such as in applications involving interactions with humans.
These requirements can be problematic for many established methods for learning
to act. In domains where the agent knows that the task instance is drawn from a
family of related tasks, albeit without access to the label of any given
instance, it can choose to act through a process of policy reuse from a
library, rather than policy learning from scratch. In policy reuse, the agent
has prior knowledge of the class of tasks in the form of a library of policies
that were learnt from sample task instances during an offline training phase.
We formalise the problem of policy reuse, and present an algorithm for
efficiently responding to a novel task instance by reusing a policy from the
library of existing policies, where the choice is based on observed 'signals'
which correlate to policy performance. We achieve this by posing the problem as
a Bayesian choice problem with a corresponding notion of an optimal response,
but the computation of that response is in many cases intractable. Therefore,
to reduce the computation cost of the posterior, we follow a Bayesian
optimisation approach and define a set of policy selection functions, which
balance exploration in the policy library against exploitation of previously
tried policies, together with a model of expected performance of the policy
library on their corresponding task instances. We validate our method in
several simulated domains of interactive, short-duration episodic tasks,
showing rapid convergence in unknown task variations.Comment: 32 pages, submitted to the Machine Learning Journa
Interactive social recommendation
National Research Foundation (NRF) Singapore under its International Research Centres in Singapore Funding Initiativ