312 research outputs found
Stochastic Subgradient Algorithms for Strongly Convex Optimization over Distributed Networks
We study diffusion and consensus based optimization of a sum of unknown
convex objective functions over distributed networks. The only access to these
functions is through stochastic gradient oracles, each of which is only
available at a different node, and a limited number of gradient oracle calls is
allowed at each node. In this framework, we introduce a convex optimization
algorithm based on the stochastic gradient descent (SGD) updates. Particularly,
we use a carefully designed time-dependent weighted averaging of the SGD
iterates, which yields a convergence rate of
after gradient updates for each node on
a network of nodes. We then show that after gradient oracle calls, the
average SGD iterate achieves a mean square deviation (MSD) of
. This rate of convergence is optimal as it
matches the performance lower bound up to constant terms. Similar to the SGD
algorithm, the computational complexity of the proposed algorithm also scales
linearly with the dimensionality of the data. Furthermore, the communication
load of the proposed method is the same as the communication load of the SGD
algorithm. Thus, the proposed algorithm is highly efficient in terms of
complexity and communication load. We illustrate the merits of the algorithm
with respect to the state-of-art methods over benchmark real life data sets and
widely studied network topologies
A kurtosis-driven variable step-size LMS algorithm
Published versio
Almost sure exponential stability of the Euler–Maruyama approximations for stochastic functional differential equations
By the continuous and discrete nonnegative semimartingale convergence theorems, this paper investigates conditions under which the Euler–Maruyama (EM) approximations of stochastic functional differential equations (SFDEs) can share the almost sure exponential stability of the exact solution. Moreover, for sufficiently small stepsize, the decay rate as measured by the Lyapunov exponent can be reproduced arbitrarily accurately
Almost sure exponential stability of numerical solutions for stochastic delay differential equations
Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (SDDEs). The important feature of this technique is that it enables us to study the almost sure exponential stability of numerical solutions of SDDEs directly. This is significantly different from most traditional methods by which the almost sure exponential stability is derived from the moment stability by the Chebyshev inequality and the Borel–Cantelli lemma
Distributive Stochastic Learning for Delay-Optimal OFDMA Power and Subband Allocation
In this paper, we consider the distributive queue-aware power and subband
allocation design for a delay-optimal OFDMA uplink system with one base
station, users and independent subbands. Each mobile has an uplink
queue with heterogeneous packet arrivals and delay requirements. We model the
problem as an infinite horizon average reward Markov Decision Problem (MDP)
where the control actions are functions of the instantaneous Channel State
Information (CSI) as well as the joint Queue State Information (QSI). To
address the distributive requirement and the issue of exponential memory
requirement and computational complexity, we approximate the subband allocation
Q-factor by the sum of the per-user subband allocation Q-factor and derive a
distributive online stochastic learning algorithm to estimate the per-user
Q-factor and the Lagrange multipliers (LM) simultaneously and determine the
control actions using an auction mechanism. We show that under the proposed
auction mechanism, the distributive online learning converges almost surely
(with probability 1). For illustration, we apply the proposed distributive
stochastic learning framework to an application example with exponential packet
size distribution. We show that the delay-optimal power control has the {\em
multi-level water-filling} structure where the CSI determines the instantaneous
power allocation and the QSI determines the water-level. The proposed algorithm
has linear signaling overhead and computational complexity ,
which is desirable from an implementation perspective.Comment: To appear in Transactions on Signal Processin
Almost sure and moment exponential stability of Euler-Maruyama discretizations for hybrid stochastic differential equations
Positive results are derived concerning the long time dynamics of numerical simulations of stochastic differential equation systems with Markovian switching. Euler-Maruyama discretizations are shown to capture almost sure and momente xponential stability for all sufficiently small timesteps under appropriate conditions
A robust quasi-newton adaptive filtering algorithm for impulse noise suppression
This paper studies the problem of robust adaptive filtering in impulse noise environment using the Quasi-Newton (QN) adaptive filtering algorithm. An M-estimate based cost function is minimized instead of the commonly used mean square error (MSE) to suppress the adverse effect of the impulse noise on the filter coefficients. In particular, a new robust quasi-Newton (R-QN) algorithm using the self-scaling variable metric (SSV) method for unconstrained optimization is studied in details. Simulation results show that the R-QN algorithm is more robust to impulse noise in the desired signal than the RLS algorithm and other QN algorithm considered. Its initial convergence speed and tracking ability to sudden system change are also superior to those of the quasi-Newton algorithm proposed in [1].published_or_final_versio
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