We consider a class of Wasserstein distributionally robust Nash equilibrium problems,
where agents construct heterogeneous data-driven Wasserstein ambiguity sets using private samples and radii, in line with their individual risk-averse behaviour. By leveraging relevant properties
of this class of games, we show that equilibria of the original seemingly infinite-dimensional
problem can be obtained as a solution to a finite-dimensional Nash equilibrium problem. We
then reformulate the problem as a finite-dimensional variational inequality and establish the
connection between the corresponding solution sets. Our reformulation has scalable behaviour
with respect to the data size and maintains a fixed number of constraints, independently of the
number of samples. To compute a solution, we leverage two algorithms, based on the golden
ratio algorithm. The efficiency of both algorithmic schemes is corroborated through extensive
simulation studies on an illustrative example and a stochastic portfolio allocation game, where
behavioural coupling among investors is modeled.@en

We consider the extension of the adaptive Golden RAtio ALgorithm (aGRAAL) for variational inequalities. We show that by selecting the momentum parameter beyond the golden ratio the convergence speed can be improved, which motivates us to study the switching between small and large momentum parameters to accelerate convergence. We validate the performance of our proposed algorithms on several classes of variational inequality problems studied in the machine learning literature, including Nash equilibrium, feasibility problem, composite minimization, Markov decision processes, and zero-sum games, and compare them to existing methods.@en

We study the data-driven finite-horizon linear quadratic regularization (LQR) problem reformulated as a semidefinite program (SDP). Our contribution is to propose two novel accelerated first-order methods for solving the resulting SDP. Our methods enjoy adaptive stepsize and adaptive smoothing parameters that speed up convergence and in turn, enhance scalability. Finally, we compare our accelerated first-order methods and show their benefits via numerical simulations on a benchmark LQR example.

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