Inverse optimal control can be used to characterize behavior in sequential decisionmaking tasks. Most existing work, however, is limited to fully observable or linear systems, or requires the action signals to be known. Here, we introduce a probabilistic approach to inverse optimal control for partially observable stochastic non-linear systems with unobserved action signals, which unifies previous approaches to inverse optimal control with maximum causal entropy formulations. Using an explicit model of the noise characteristics of the sensory and motor systems of the agent in conjunction with local linearization techniques, we derive an approximate likelihood function for the model parameters, which can be computed within a single forward pass.

We analyze the convergence rates of stochastic gradient algorithms for smooth finite-sum minimax optimization and show that, for many such algorithms, sampling the data points without replacement leads to faster convergence compared to sampling with replacement. For the smooth and strongly convex-strongly concave setting, we consider gradient descent ascent and the proximal point method, and present a unified analysis of two popular without-replacement sampling strategies, namely Random Reshuffling (RR), which shuffles the data every epoch, and Single Shuffling or Shuffle Once (SO), which shuffles only at the beginning. We obtain tight convergence rates for RR and SO and demonstrate that these strategies lead to faster convergence than uniform sampling. Moving beyond convexity, we obtain similar results for smooth nonconvex-nonconcave objectives satisfying a two-sided Polyak-Łojasiewicz inequality. Finally, we demonstrate that our techniques are general enough to analyze the effect of data-ordering attacks, where an adversary manipulates the order in which data points are supplied to the optimizer. Our analysis also recovers tight rates for the incremental gradient method, where the data points are not shuffled at all.

As shown in the main text, under the assumption that the influence network is unbiased, our factor baselines are indeed valid control variates. We prove this result below, repeating the statement itself for posterity and providing a supplementary lemma on control variates as a restatement of known results. Let X, Y and Zbe random variables where the law of Xconditional on Z is denoted Pθ(X|Z), and Y is independent of X conditioned on Z; i.e. Then, we have that E[Y θln Pθ(X)] = 0. Proof. Factor baselines are valid control variates if GΣ is true to the MDP (i.e.

The detailed architecture for VanillaNet with 7-13 layers can be found in Table 1, where each convolutional layer is followed with an activation function. For the VanillaNet-13-1.5, the number of channels are multiplied with 1.5. For classification on ImageNet, we train the VanillaNets for 300 epochs utilizing the cosine learning rate decay [5]. The λis linearly decayed from 1 to 0 on epoch 0 and 100, respectively. The training details can be fould in Table 2.

At the heart of foundation models is the philosophy of "more is different", exemplified by the astonishing success in computer vision and natural language processing. However, the challenges of optimization and inherent complexity of transformer models call for a paradigm shift towards simplicity. In this study, we introduce VanillaNet, a neural network architecture that embraces elegance in design. By avoiding high depth, shortcuts, and intricate operations like selfattention, VanillaNet is refreshingly concise yet remarkably powerful. Each layer is carefully crafted to be compact and straightforward, with nonlinear activation functions pruned after training to restore the original architecture. VanillaNet overcomes the challenges of inherent complexity, making it ideal for resourceconstrained environments. Its easy-to-understand and highly simplified architecture opens new possibilities for efficient deployment. Extensive experimentation demonstrates that VanillaNet delivers performance on par with renowned deep neural networks and vision transformers, showcasing the power of minimalism in deep learning. This visionary journey of VanillaNet has significant potential to redefine the landscape and challenge the status quo of foundation model, setting a new path for elegant and effective model design.