Finite-Horizon Random-Reshuffling Optimizer

1. Integration point: modify the dataloader or sampler feeding the optimizer, not the neural-network architecture or loss. At the beginning of each epoch, generate a fresh random permutation of all training indices. Partition that permutation into minibatches of size B and perform one update per minibatch. For a fair first test, use identical models, batch sizes, learning-rate schedules, augmentations, and optimizer hyperparameters in the random-reshuffling and baseline conditions. 2. Pseudocode: for epoch in range(E): perm = randperm(N); for ids in chunks(perm,B): loss = mean(loss_i(model(x[i]),y[i]) for i in ids); g = grad(loss,theta); v = beta*v + g; theta = theta - eta*v. Here perm represents pi_e, each per-example loss is f_i, B is minibatch size, eta is the minibatch stepsize, and v is optional momentum. Do not sample replacement indices inside an epoch. 3. The finite-sum objective and smoothness condition come from the paper; no theorem constant is available in the extracted material. If adaptive stepsizes are tested, estimate a local smoothness proxy with gradient-difference probes: L_hat = norm(g(theta+delta)-g(theta))/norm(delta). 4. First cheap experiment: train an MLP on MNIST and ResNet-18 on CIFAR-10, comparing ordinary shuffled minibatch SGD, random-reshuffling minibatches, and random reshuffling with momentum for 5, 20, and 100 epochs over at least five random seeds. Plot training loss, test accuracy, gradient norm, and wall-clock time versus examples processed. A successful result is lower loss or higher accuracy at equal examples processed, particularly during early epochs, while remaining stable at learning rates where ordinary SGD is noisier; additionally test whether random reshuffling avoids any learning-rate reduction proportional to dataset size.