# Regret Minimization

Multi-agent learning in continuous general-sum games has long struggled with non-stationarity, because agents maximizing their own payoffs make the learning target move. DRAC shifts the objective from payoff maximization to regret minimization, fixing opponents' actions and sampling unilateral deviations to build a stationary regret target, with a dual-head critic predicting best-response utility and regret separately. In a three-agent, five-round sequential Cournot oligopoly and a two-agent, five-stage proportional prize contest, DRAC's exploitability converged to 1.37×10⁻⁴ and 7.45×10⁻⁴, with mean relative absolute deviations of 0.011 and 0.030, both below MADDPG at the same training budget.

Multi-agent learning in continuous general-sum games has long struggled with non-stationarity, because agents maximizing their own payoffs make the learning target move. DRAC shifts the objective from payoff maximization to regret minimization, fixing opponents' actions and sampling unilateral deviations to build a stationary regret target, with a dual-head critic predicting best-response utility and regret separately. In a three-agent, five-round sequential Cournot oligopoly and a two-agent, five-stage proportional prize contest, DRAC's exploitability converged to 1.37×10⁻⁴ and 7.45×10⁻⁴, with mean relative absolute deviations of 0.011 and 0.030, both below MADDPG at the same training budget.

Adaptive task allocation previously came with guarantees only when worker computation times stay fixed, yet in shared clusters resource contention, background jobs, or network congestion can turn a fast worker into a straggler and invalidate the allocation. Sliding Window Adaptive Task Allocation (SW-ATA) estimates each worker's delay mean from a recent window of observations and picks allocations from lower confidence bounds, so it can track fast workers while the delay distribution changes from round to round. On synthetic drifting-delay distributed stochastic optimization, it clearly beats the original adaptive allocation and uniform allocation, stays close to an oracle that knows the true means, and uses the least worker time.

Adaptive task allocation previously came with guarantees only when worker computation times stay fixed, yet in shared clusters resource contention, background jobs, or network congestion can turn a fast worker into a straggler and invalidate the allocation. Sliding Window Adaptive Task Allocation (SW-ATA) estimates each worker's delay mean from a recent window of observations and picks allocations from lower confidence bounds, so it can track fast workers while the delay distribution changes from round to round. On synthetic drifting-delay distributed stochastic optimization, it clearly beats the original adaptive allocation and uniform allocation, stays close to an oracle that knows the true means, and uses the least worker time.