Randomized gradient-free methods for distributed aggregative optimization with application to robotic coordination

The objective of this thesis is to propose, implement and analyze novel algorithms that integrate Zeroth-Order optimization techniques with gradient tracking methods to solve distributed aggregative optimization problems in multi-agent systems. Traditional gradient-based methods require explicit derivative information, which is often unavailable in real-world scenarios involving black-box or noisy objectives. Instead, Zeroth-Order methods overcome this limitation by estimating gradients through finite-difference approximations, enabling optimization using only function evaluations. We extend this approach to a distributed aggregative setting, where agents collaborate over a strongly connected network to minimize a global objective composed of locally known cost functions, adding a global variable into the procedure. We consider two approximation schemes, implementing a causal aggregative variant of the distributed gradient tracking algorithm, ensuring agents reach consensus and minimize the global cost function. The analysis and the simulations validate the performance of the proposed schemes, highlighting the trade-offs between computational efficiency, approximation accuracy, and convergence speed.