399 research outputs found
Non-Stochastic Control with Bandit Feedback
We study the problem of controlling a linear dynamical system with
adversarial perturbations where the only feedback available to the controller
is the scalar loss, and the loss function itself is unknown. For this problem,
with either a known or unknown system, we give an efficient sublinear regret
algorithm. The main algorithmic difficulty is the dependence of the loss on
past controls. To overcome this issue, we propose an efficient algorithm for
the general setting of bandit convex optimization for loss functions with
memory, which may be of independent interest
Algebraic Methods in the Congested Clique
In this work, we use algebraic methods for studying distance computation and
subgraph detection tasks in the congested clique model. Specifically, we adapt
parallel matrix multiplication implementations to the congested clique,
obtaining an round matrix multiplication algorithm, where
is the exponent of matrix multiplication. In conjunction
with known techniques from centralised algorithmics, this gives significant
improvements over previous best upper bounds in the congested clique model. The
highlight results include:
-- triangle and 4-cycle counting in rounds, improving upon the
triangle detection algorithm of Dolev et al. [DISC 2012],
-- a -approximation of all-pairs shortest paths in
rounds, improving upon the -round -approximation algorithm of Nanongkai [STOC 2014], and
-- computing the girth in rounds, which is the first
non-trivial solution in this model.
In addition, we present a novel constant-round combinatorial algorithm for
detecting 4-cycles.Comment: This is work is a merger of arxiv:1412.2109 and arxiv:1412.266
Communication Efficient Checking of Big Data Operations
We propose fast probabilistic algorithms with low (i.e., sublinear in the
input size) communication volume to check the correctness of operations in Big
Data processing frameworks and distributed databases. Our checkers cover many
of the commonly used operations, including sum, average, median, and minimum
aggregation, as well as sorting, union, merge, and zip. An experimental
evaluation of our implementation in Thrill (Bingmann et al., 2016) confirms the
low overhead and high failure detection rate predicted by theoretical analysis
Maintaining Triangle Queries under Updates
We consider the problem of incrementally maintaining the triangle queries
with arbitrary free variables under single-tuple updates to the input
relations. We introduce an approach called IVM that exhibits a
trade-off between the update time, the space, and the delay for the enumeration
of the query result, such that the update time ranges from the square root to
linear in the database size while the delay ranges from constant to linear
time. IVM achieves Pareto worst-case optimality in the update-delay
space conditioned on the Online Matrix-Vector Multiplication conjecture. It is
strongly Pareto optimal for the triangle queries with zero or three free
variables and weakly Pareto optimal for the triangle queries with one or two
free variables.Comment: 47 pages, 18 figure
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