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Tight Analyses for Non-Smooth Stochastic Gradient Descent

It is proved that after $T$ steps of stochastic gradient descent, the error of the final iterate is $O(\log(T)/T)$ with high probability, and there exists a function from this class for which the errors of the last iterate of deterministic gradient descent is $\Omega(\log (T)/\sqrt{T})$.
arXiv (opens in a new tab)

Approximating submodular functions everywhere

The problem of approximating a non-negative, monotone, submodular function f on a ground set of size n everywhere is considered, after only poly(n) oracle queries, and it is shown that no algorithm can achieve a factor better than Ω(√n/log n), even for rank functions of a matroid.
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Semi-matchings for bipartite graphs and load balancing

Publisher (opens in a new tab)

On the capacity of information networks

An outer bound on the rate region of noise-free information networks is given and it is shown that multicommodity flow solutions achieve the capacity in an infinite class of undirected graphs, thereby making progress on a conjecture of Li and Li.
ACM (opens in a new tab)

An Algorithmic Proof of the Lovasz Local Lemma via Resampling Oracles

It is shown that, in all scenarios to which the original Lovasz Local Lemma applies, there exist resampling oracles, although they are not necessarily efficient, and for essentially all known applications of the LovasZ Local LemMA and its generalizations, these oracles are designed.
IEEE (opens in a new tab)

Non-Adaptive Fault Diagnosis for All-Optical Networks via Combinatorial Group Testing on Graphs

This work considers the problem of detecting failures for all-optical networks, and considers a non-adaptive approach where all the probes are sent in parallel, to minimize the number of parallel probes, so as to keep network cost low.
IEEE (opens in a new tab)

Deterministic network coding by matrix completion

A new deterministic algorithm to construct network codes for multicast problems, a particular class of network information ow problems, based on a new algorithm for maximum-rank completion of mixed matrices, which is faster than existing deterministic algorithms and can operate over a smaller field.
ACM (opens in a new tab)

Learning submodular functions

To prove the general lower bound of Omega(n1/3), a surprising Omega(n1/3) lower bound is provided based on a new interesting class of matroids based on lossless expanders which can take wildly varying rank values on superpolynomially many sets; no such construction was previously known.
ACM (opens in a new tab)

Algebraic Algorithms for Matching and Matroid Problems

New algebraic approaches for two well-known combinatorial problems: nonbipartite matching and matroid intersection are presented and new randomized algorithms that exceed or match the efficiency of existing algorithms are yielded.
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Sketching and Streaming Entropy via Approximation Theory

This work gives near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions, and yields the best-known and near-Optimal additive approximations for entropy, and hence also for conditional entropy and mutual information.
IEEE (opens in a new tab)
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