arXiv subjects

Abhinav Aggarwal

Publications and source records attributed to Abhinav Aggarwal.

21 records · Page 2Linked to original sources

arXiv2017

Beating the Multiplicative Weights Update Algorithm

Multiplicative weights update algorithms have been used extensively in designing iterative algorithms for many computational tasks. The core idea is to maintain a distribution over a set of experts and update this distribution in an online fashion based on the parameters of the underlying optimization problem. In this report, we study the behavior of a special MWU algorithm used for generating a global coin flip in the presence of an adversary that tampers the experts' advice. Specifically, we focus our attention on two adversarial strategies: (1) non-adaptive, in which the adversary chooses a fixed set of experts a priori and corrupts their advice in each round; and (2) adaptive, in which this set is chosen as the rounds of the algorithm progress. We formulate these adversarial strategies as being greedy in terms of trying to maximize the share of the corrupted experts in the final weighted advice the MWU computes and provide the underlying optimization problem that needs to be solved to achieve this goal. We provide empirical results to show that in the presence of either of the above adversaries, the MWU algorithm takes $\mathcal{O}(n)$ rounds in expectation to produce the desired output. This result compares well with the current state of the art of $\mathcal{O}(n^3)$ for the general Byzantine consensus problem. Finally, we briefly discuss the extension of these adversarial strategies for a general MWU algorithm and provide an outline for the framework in that setting.

cs.DC↗

arXiv2017

Sending a Message with Unknown Noise

Alice and Bob are connected via a two-way channel, and Alice wants to send a message of $L$ bits to Bob. An adversary flips an arbitrary but finite number of bits, $T$, on the channel. This adversary knows our algorithm and Alice's message, but does not know any private random bits generated by Alice or Bob, nor the bits sent over the channel, except when these bits can be predicted by knowledge of Alice's message or our algorithm. We want Bob to receive Alice's message and for both players to terminate, with error probability at most $δ> 0$, where $δ$ is a parameter known to both Alice and Bob. Unfortunately, the value $T$ is unknown in advance to either Alice or Bob, and the value $L$ is unknown in advance to Bob. We describe an algorithm to solve the above problem while sending an expected $L + O \left( T + \min \left(T+1,\frac{L}{\log L} \right) \log \left( \frac{L}δ \right) \right)$ bits. A special case is when $δ= O(1/L^c)$, for some constant $c$. Then when $T = o(L/\log L)$, the expected number of bits sent is $L + o(L)$, and when $T = Ω(L)$, the expected number of bits sent is $L + O\left( T \right)$, which is asymptotically optimal.

cs.CR↗

arXiv2017

Distributed Computing with Channel Noise

A group of $n$ users want to run a distributed protocol $π$ over a network where communication occurs via private point-to-point channels. Unfortunately, an adversary, who knows $π$, is able to maliciously flip bits on the channels. Can we efficiently simulate $π$ in the presence of such an adversary? We show that this is possible, even when $L$, the number of bits sent in $π$, and $T$, the number of bits flipped by the adversary are not known in advance. In particular, we show how to create a robust version of $π$ that 1) fails with probability at most $δ$, for any $δ>0$; and 2) sends $\tilde{O}(L + T)$ bits, where the $\tilde{O}$ notation hides a $\log (nL/ δ)$ term multiplying $L$. Additionally, we show how to improve this result when the average message size $α$ is not constant. In particular, we give an algorithm that sends $O( L (1 + (1/α) \log (n L/δ) + T)$ bits. This algorithm is adaptive in that it does not require a priori knowledge of $α$. We note that if $α$ is $Ω\left( \log (n L/δ) \right)$, then this improved algorithm sends only $O(L+T)$ bits, and is therefore within a constant factor of optimal.

cs.CR↗