3 research outputs found
Improving the Convergence Rate of One-Point Zeroth-Order Optimization using Residual Feedback
Many existing zeroth-order optimization (ZO) algorithms adopt two-point
feedback schemes due to their fast convergence rate compared to one-point
feedback schemes. However, two-point schemes require two evaluations of the
objective function at each iteration, which can be impractical in applications
where the data are not all available a priori, e.g., in online optimization. In
this paper, we propose a novel one-point feedback scheme that queries the
function value only once at each iteration and estimates the gradient using the
residual between two consecutive feedback points. When optimizing a
deterministic Lipschitz function, we show that the query complexity of ZO with
the proposed one-point residual feedback matches that of ZO with the existing
two-point feedback schemes. Moreover, the query complexity of the proposed
algorithm can be improved when the objective function has Lipschitz gradient.
Then, for stochastic bandit optimization problems, we show that ZO with
one-point residual feedback achieves the same convergence rate as that of ZO
with two-point feedback with uncontrollable data samples. We demonstrate the
effectiveness of the proposed one-point residual feedback via extensive
numerical experiments
Convergence Analysis of Nonconvex Distributed Stochastic Zeroth-order Coordinate Method
This paper investigates the stochastic distributed nonconvex optimization
problem of minimizing a global cost function formed by the summation of
local cost functions. We solve such a problem by involving zeroth-order (ZO)
information exchange. In this paper, we propose a ZO distributed primal-dual
coordinate method (ZODIAC) to solve the stochastic optimization problem. Agents
approximate their own local stochastic ZO oracle along with coordinates with an
adaptive smoothing parameter. We show that the proposed algorithm achieves the
convergence rate of for general nonconvex cost
functions. We demonstrate the efficiency of proposed algorithms through a
numerical example in comparison with the existing state-of-the-art centralized
and distributed ZO algorithms
Zeroth-Order Algorithms for Stochastic Distributed Nonconvex Optimization
In this paper, we consider a stochastic distributed nonconvex optimization
problem with the cost function being distributed over agents having access
only to zeroth-order (ZO) information of the cost. This problem has various
machine learning applications. As a solution, we propose two distributed ZO
algorithms, in which at each iteration each agent samples the local stochastic
ZO oracle at two points with an adaptive smoothing parameter. We show that the
proposed algorithms achieve the linear speedup convergence rate
for smooth cost functions and
convergence rate when the global cost function
additionally satisfies the Polyak--Lojasiewicz (P--L) condition, where and
are the dimension of the decision variable and the total number of
iterations, respectively. To the best of our knowledge, this is the first
linear speedup result for distributed ZO algorithms, which enables systematic
processing performance improvements by adding more agents. We also show that
the proposed algorithms converge linearly when considering deterministic
centralized optimization problems under the P--L condition. We demonstrate
through numerical experiments the efficiency of our algorithms on generating
adversarial examples from deep neural networks in comparison with baseline and
recently proposed centralized and distributed ZO algorithms