2,926 research outputs found
Overcommitment in Cloud Services -- Bin packing with Chance Constraints
This paper considers a traditional problem of resource allocation, scheduling
jobs on machines. One such recent application is cloud computing, where jobs
arrive in an online fashion with capacity requirements and need to be
immediately scheduled on physical machines in data centers. It is often
observed that the requested capacities are not fully utilized, hence offering
an opportunity to employ an overcommitment policy, i.e., selling resources
beyond capacity. Setting the right overcommitment level can induce a
significant cost reduction for the cloud provider, while only inducing a very
low risk of violating capacity constraints. We introduce and study a model that
quantifies the value of overcommitment by modeling the problem as a bin packing
with chance constraints. We then propose an alternative formulation that
transforms each chance constraint into a submodular function. We show that our
model captures the risk pooling effect and can guide scheduling and
overcommitment decisions. We also develop a family of online algorithms that
are intuitive, easy to implement and provide a constant factor guarantee from
optimal. Finally, we calibrate our model using realistic workload data, and
test our approach in a practical setting. Our analysis and experiments
illustrate the benefit of overcommitment in cloud services, and suggest a cost
reduction of 1.5% to 17% depending on the provider's risk tolerance
Gossip Dual Averaging for Decentralized Optimization of Pairwise Functions
In decentralized networks (of sensors, connected objects, etc.), there is an
important need for efficient algorithms to optimize a global cost function, for
instance to learn a global model from the local data collected by each
computing unit. In this paper, we address the problem of decentralized
minimization of pairwise functions of the data points, where these points are
distributed over the nodes of a graph defining the communication topology of
the network. This general problem finds applications in ranking, distance
metric learning and graph inference, among others. We propose new gossip
algorithms based on dual averaging which aims at solving such problems both in
synchronous and asynchronous settings. The proposed framework is flexible
enough to deal with constrained and regularized variants of the optimization
problem. Our theoretical analysis reveals that the proposed algorithms preserve
the convergence rate of centralized dual averaging up to an additive bias term.
We present numerical simulations on Area Under the ROC Curve (AUC) maximization
and metric learning problems which illustrate the practical interest of our
approach
Correlation Decay in Random Decision Networks
We consider a decision network on an undirected graph in which each node
corresponds to a decision variable, and each node and edge of the graph is
associated with a reward function whose value depends only on the variables of
the corresponding nodes. The goal is to construct a decision vector which
maximizes the total reward. This decision problem encompasses a variety of
models, including maximum-likelihood inference in graphical models (Markov
Random Fields), combinatorial optimization on graphs, economic team theory and
statistical physics. The network is endowed with a probabilistic structure in
which costs are sampled from a distribution. Our aim is to identify sufficient
conditions to guarantee average-case polynomiality of the underlying
optimization problem. We construct a new decentralized algorithm called Cavity
Expansion and establish its theoretical performance for a variety of models.
Specifically, for certain classes of models we prove that our algorithm is able
to find near optimal solutions with high probability in a decentralized way.
The success of the algorithm is based on the network exhibiting a correlation
decay (long-range independence) property. Our results have the following
surprising implications in the area of average case complexity of algorithms.
Finding the largest independent (stable) set of a graph is a well known NP-hard
optimization problem for which no polynomial time approximation scheme is
possible even for graphs with largest connectivity equal to three, unless P=NP.
We show that the closely related maximum weighted independent set problem for
the same class of graphs admits a PTAS when the weights are i.i.d. with the
exponential distribution. Namely, randomization of the reward function turns an
NP-hard problem into a tractable one
Regret-Minimization Algorithms for Multi-Agent Cooperative Learning Systems
A Multi-Agent Cooperative Learning (MACL) system is an artificial
intelligence (AI) system where multiple learning agents work together to
complete a common task. Recent empirical success of MACL systems in various
domains (e.g. traffic control, cloud computing, robotics) has sparked active
research into the design and analysis of MACL systems for sequential decision
making problems. One important metric of the learning algorithm for decision
making problems is its regret, i.e. the difference between the highest
achievable reward and the actual reward that the algorithm gains. The design
and development of a MACL system with low-regret learning algorithms can create
huge economic values. In this thesis, I analyze MACL systems for different
sequential decision making problems. Concretely, the Chapter 3 and 4
investigate the cooperative multi-agent multi-armed bandit problems, with
full-information or bandit feedback, in which multiple learning agents can
exchange their information through a communication network and the agents can
only observe the rewards of the actions they choose. Chapter 5 considers the
communication-regret trade-off for online convex optimization in the
distributed setting. Chapter 6 discusses how to form high-productive teams for
agents based on their unknown but fixed types using adaptive incremental
matchings. For the above problems, I present the regret lower bounds for
feasible learning algorithms and provide the efficient algorithms to achieve
this bound. The regret bounds I present in Chapter 3, 4 and 5 quantify how the
regret depends on the connectivity of the communication network and the
communication delay, thus giving useful guidance on design of the communication
protocol in MACL systemsComment: Thesis submitted to London School of Economics and Political Science
for PhD in Statistic
When is the individually rational payoff in a repeated game equal to the minmax payoff?
We study the relationship between a player’s (stage game) minmax payoff and the individually rational payoff in repeated games with imperfect monitoring. We characterize the signal structures under which these two payoffs coincide for any payoff matrix. Under a full rank assumption, we further show that, if the monitoring structure of an infinitely repeated game ‘nearly’ satisfies this condition, then these two payoffs are approximately equal, independently of the discount factor. This provides conditions under which existing folk theorems exactly characterize the limiting payoff set.
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