12 research outputs found
On Speed and Advantage : Results in Information Velocity and Monitoring Problems
No full textInformation theory has allowed us to determine the fundamental limit of various communication and algorithmic problems, e.g., the channel coding problem, the compression problem, and the hypothesis testing problem. In this work, we revisit the assumptions underlying two of the classical information theoretic problems: the channel coding problem and the hypothesis testing problem.
In the first part, we study the information velocity problem. If the channel coding problem answers the question of how much information we can send per time unit, the information velocity problem tackles the question of the latency of communicating said information on a communication network composed of relays. In the literature, this problem is commonly studied in the regime of finite message size but with a growing number of relays. In this work, we consider an asymptotic regime where we let the message size to grow to infinity. We present a converse result and two achievability results: one for Binary Erasure Channels (BEC) and one for Additive White Gaussian Noise (AWGN) channels with feedback. The converse result is obtained by extending the argument given in (Rajagopalan and Schulman, 1994) using the tools of F-divergences. The achievability results that we obtain are based on two different ideas. In the achievability result for BEC, we exploited the property of tree codes which ensure that all message bits can eventually be correctly decoded after a certain time delay. We use this property to build a tape abstraction which allows for the streaming of message bits through the relay chain. For AWGN channels, we modify the Schalkwijk-Kailath scheme to allow each relay to focus on locally transmitting its estimate of the message bits to its neighboring relay. We analyze the local behavior of this scheme, and show that we can prove results about the information velocity of the whole network based on these local results.
In the second part we study the monitoring problem. This problem capture a scenario where several regular data-generating processes maximize their own reward, with one adversarial data-generating process hiding among these regular processes and privy to certain private information. This model introduces an interesting trade-off where the adversarial data-generating process aims to exploit its private information without deviating too much from the regular data-generating processes. As by increasing its deviation, it also becomes more distinguishable from the regular data generating processes. We will analyze this problem using tools from information theory and characterize the extent of the advantage that can be obtained by the adversarial data generation process. In doing so, we showed that classification problems, which are commonly modeled as hypothesis testing problems, become more complex when an adversarial data-generating process can adapt to the tester's protocol.LTH
Safety in Numbers: Asymptotic Analysis of a Monitoring Problem
No full textIn this work, we introduce a setup where a monitoring entity attempts to distinguish a cheating player among a group of regular players where all players behave in order to maximize their reward. We assume that the cheating player has an "information advantage" compared to the regular players. However, greedily exploiting this advantage will lead to the cheating player being easily distinguishable from its peers. Hence there is a tension between exploitation of the said advantage and the probability of being caught. We characterize this trade-off showing that the cheating player can obtain a higher reward as the number of regular players grows. We also show that, under a certain regime, a monitoring strategy based on the empirical divergence function attains the same normalized reward as the minimax reward.LTH
Safety in Numbers: Asymptotic Analysis of a Monitoring Problem
No full textIn this work, we introduce a setup where a monitoring entity attempts to distinguish a cheating player among a group of regular players where all players behave in order to maximize their reward. We assume that the cheating player has an ``information advantage'' compared to the regular players. However, greedily exploiting this advantage will lead to the cheating player being easily distinguishable from its peers. Hence there is a tension between exploitation of the said advantage and the probability of being caught. We characterize this trade-off showing that the cheating player can obtain a higher reward as the number of regular players grows. We also show that, under a certain regime, a monitoring strategy based on the empirical divergence function attains the same normalized reward as the minimax reward.LTH
Optimal Policies for Age and Distortion in a Discrete-Time Model
No full textWe propose a simple model to study the tradeoff between timeliness and distortion, where different pieces of data have a different cost of not being sent. We pose the question of finding the optimal tradeoff as a policy design problem amenable to dynamic programming methods. We study the structural properties of optimal transmission policies, give an algorithmic procedure to find the optimal tradeoff, and numerically evaluate some instances.LTH
COVERAGE CONTROL ON MULTI-AGENT SYSTEM
No full textIn this work, we study the problem of maximizing the coverage of a Mobile Sensor
Network under an unknown interest function through distributed means. To maximize
the coverage, we adopt the distributed version of the Voronoi locational optimization
method. The stability results of the method is discussed. Numerical experiment is conducted
to study the eect of network topology and interest function. To estimate the
interest function, we used the distributed Recursive Least Square method based on Alternating
Minimization Algorithm Framework. The correctness and eectiveness of the
method is proved through numerical simulation. Then, we aim to combine those two
method. The condition that need to be fulfilled to make the system stable is discussed.
We also introduced some modification to the RLS algorithm to alleviate the problem
of the lack of excitation. The combined algorithm is then simulated to show its eectiveness.
The result of this work shows that the modified method perform slightly worse
compared with the case of centralized locational optimization with known interest fiel
Optimal Policies for Age and Distortion in a Discrete-Time Model
No full textWe propose a simple model to study the tradeoff between timeliness and distortion, where different pieces of data have a different cost of not being sent. We pose the question of finding the optimal tradeoff as a policy design problem amenable to dynamic programming methods. We study the structural properties of optimal transmission policies, give an algorithmic procedure to find the optimal tradeoff, and numerically evaluate some instances.LTH
Disturbance Rejection for Quadrotor Attitude Control Based on PD and Fuzzy Logic Algorithm
No full text
