357 research outputs found
Dispersion for Data-Driven Algorithm Design, Online Learning, and Private Optimization
Data-driven algorithm design, that is, choosing the best algorithm for a
specific application, is a crucial problem in modern data science.
Practitioners often optimize over a parameterized algorithm family, tuning
parameters based on problems from their domain. These procedures have
historically come with no guarantees, though a recent line of work studies
algorithm selection from a theoretical perspective. We advance the foundations
of this field in several directions: we analyze online algorithm selection,
where problems arrive one-by-one and the goal is to minimize regret, and
private algorithm selection, where the goal is to find good parameters over a
set of problems without revealing sensitive information contained therein. We
study important algorithm families, including SDP-rounding schemes for problems
formulated as integer quadratic programs, and greedy techniques for canonical
subset selection problems. In these cases, the algorithm's performance is a
volatile and piecewise Lipschitz function of its parameters, since tweaking the
parameters can completely change the algorithm's behavior. We give a sufficient
and general condition, dispersion, defining a family of piecewise Lipschitz
functions that can be optimized online and privately, which includes the
functions measuring the performance of the algorithms we study. Intuitively, a
set of piecewise Lipschitz functions is dispersed if no small region contains
many of the functions' discontinuities. We present general techniques for
online and private optimization of the sum of dispersed piecewise Lipschitz
functions. We improve over the best-known regret bounds for a variety of
problems, prove regret bounds for problems not previously studied, and give
matching lower bounds. We also give matching upper and lower bounds on the
utility loss due to privacy. Moreover, we uncover dispersion in auction design
and pricing problems
Coordination Complexity: Small Information Coordinating Large Populations
We initiate the study of a quantity that we call coordination complexity. In a distributed optimization problem, the information defining a problem instance is distributed among n parties, who need to each choose an action, which jointly will form a solution to the optimization problem. The coordination complexity represents the minimal amount of information that a centralized coordinator, who has full knowledge of the problem instance, needs to broadcast in order to coordinate the n parties to play a nearly optimal solution.
We show that upper bounds on the coordination complexity of a problem imply the existence of good jointly differentially private algorithms for solving that problem, which in turn are known to upper bound the price of anarchy in certain games with dynamically changing populations.
We show several results. We fully characterize the coordination complexity for the problem of computing a many-to-one matching in a bipartite graph. Our upper bound in fact extends much more generally to the problem of solving a linearly separable convex program. We also give a different upper bound technique, which we use to bound the coordination complexity of coordinating a Nash equilibrium in a routing game, and of computing a stable matching
Differentially Private Optimal Power Flow for Distribution Grids
Although distribution grid customers are obliged to share their consumption
data with distribution system operators (DSOs), a possible leakage of this data
is often disregarded in operational routines of DSOs. This paper introduces a
privacy-preserving optimal power flow (OPF) mechanism for distribution grids
that secures customer privacy from unauthorised access to OPF solutions, e.g.,
current and voltage measurements. The mechanism is based on the framework of
differential privacy that allows to control the participation risks of
individuals in a dataset by applying a carefully calibrated noise to the output
of a computation. Unlike existing private mechanisms, this mechanism does not
apply the noise to the optimization parameters or its result. Instead, it
optimizes OPF variables as affine functions of the random noise, which weakens
the correlation between the grid loads and OPF variables. To ensure feasibility
of the randomized OPF solution, the mechanism makes use of chance constraints
enforced on the grid limits. The mechanism is further extended to control the
optimality loss induced by the random noise, as well as the variance of OPF
variables. The paper shows that the differentially private OPF solution does
not leak customer loads up to specified parameters
- …