11,930 research outputs found
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
A Two-Level Approach to Large Mixed-Integer Programs with Application to Cogeneration in Energy-Efficient Buildings
We study a two-stage mixed-integer linear program (MILP) with more than 1
million binary variables in the second stage. We develop a two-level approach
by constructing a semi-coarse model (coarsened with respect to variables) and a
coarse model (coarsened with respect to both variables and constraints). We
coarsen binary variables by selecting a small number of pre-specified daily
on/off profiles. We aggregate constraints by partitioning them into groups and
summing over each group. With an appropriate choice of coarsened profiles, the
semi-coarse model is guaranteed to find a feasible solution of the original
problem and hence provides an upper bound on the optimal solution. We show that
solving a sequence of coarse models converges to the same upper bound with
proven finite steps. This is achieved by adding violated constraints to coarse
models until all constraints in the semi-coarse model are satisfied. We
demonstrate the effectiveness of our approach in cogeneration for buildings.
The coarsened models allow us to obtain good approximate solutions at a
fraction of the time required by solving the original problem. Extensive
numerical experiments show that the two-level approach scales to large problems
that are beyond the capacity of state-of-the-art commercial MILP solvers
Turbo-Aggregate: Breaking the Quadratic Aggregation Barrier in Secure Federated Learning
Federated learning is a distributed framework for training machine learning
models over the data residing at mobile devices, while protecting the privacy
of individual users. A major bottleneck in scaling federated learning to a
large number of users is the overhead of secure model aggregation across many
users. In particular, the overhead of the state-of-the-art protocols for secure
model aggregation grows quadratically with the number of users. In this paper,
we propose the first secure aggregation framework, named Turbo-Aggregate, that
in a network with users achieves a secure aggregation overhead of
, as opposed to , while tolerating up to a user dropout
rate of . Turbo-Aggregate employs a multi-group circular strategy for
efficient model aggregation, and leverages additive secret sharing and novel
coding techniques for injecting aggregation redundancy in order to handle user
dropouts while guaranteeing user privacy. We experimentally demonstrate that
Turbo-Aggregate achieves a total running time that grows almost linear in the
number of users, and provides up to speedup over the
state-of-the-art protocols with up to users. Our experiments also
demonstrate the impact of model size and bandwidth on the performance of
Turbo-Aggregate
Reduction of Markov Chains using a Value-of-Information-Based Approach
In this paper, we propose an approach to obtain reduced-order models of
Markov chains. Our approach is composed of two information-theoretic processes.
The first is a means of comparing pairs of stationary chains on different state
spaces, which is done via the negative Kullback-Leibler divergence defined on a
model joint space. Model reduction is achieved by solving a
value-of-information criterion with respect to this divergence. Optimizing the
criterion leads to a probabilistic partitioning of the states in the high-order
Markov chain. A single free parameter that emerges through the optimization
process dictates both the partition uncertainty and the number of state groups.
We provide a data-driven means of choosing the `optimal' value of this free
parameter, which sidesteps needing to a priori know the number of state groups
in an arbitrary chain.Comment: Submitted to Entrop
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