This paper presents a periodic bipedal gait learning method using reward composition, integrated with a real-time gait planner for humanoid robots. First, we introduce a novel gait planner that incorporates dynamics to design the desired joint trajectory. In the gait design process, the 3D robot model is decoupled into two 2D models, which are then approximated as hybrid inverted pendulums (H-LIP) for trajectory planning. The gait planner operates in parallel in real time within the robot's learning environment. Second, based on this gait planner, we design three effective reward functions within a reinforcement learning framework, forming a reward composition to achieve periodic bipedal gait. This reward composition reduces the robot's learning time and enhances locomotion performance. Finally, a gait design example and performance comparison are presented to demonstrate the effectiveness of the proposed method.

Previous algorithms can solve convex-concave minimax problems $\min_{x \in \mathcal{X}} \max_{y \in \mathcal{Y}} f(x,y)$ with $\mathcal{O}(ε^{-2/3})$ second-order oracle calls using Newton-type methods. This result has been speculated to be optimal because the upper bound is achieved by a natural generalization of the optimal first-order method. In this work, we show an improved upper bound of $\tilde{\mathcal{O}}(ε^{-4/7})$ by generalizing the optimal second-order method for convex optimization to solve the convex-concave minimax problem. We further apply a similar technique to lazy Hessian algorithms and show that our proposed algorithm can also be seen as a second-order ``Catalyst'' framework (Lin et al., JMLR 2018) that could accelerate any globally convergent algorithms for solving minimax problems.

We introduce AdaAct, a novel optimization algorithm that adjusts learning rates according to activation variance. Our method enhances the stability of neuron outputs by incorporating neuron-wise adaptivity during the training process, which subsequently leads to better generalization -- a complementary approach to conventional activation regularization methods. Experimental results demonstrate AdaAct's competitive performance across standard image classification benchmarks. We evaluate AdaAct on CIFAR and ImageNet, comparing it with other state-of-the-art methods. Importantly, AdaAct effectively bridges the gap between the convergence speed of Adam and the strong generalization capabilities of SGD, all while maintaining competitive execution times. Code is available at https://github.com/hseung88/adaact.

We develop an optimization framework centered around a core idea: once a (parametric) policy is specified, control authority is transferred to the policy, resulting in an autonomous dynamical system. Thus we should be able to optimize policy parameters without further reference to controls or actions, and without directly using the machinery of approximate Dynamic Programming and Reinforcement Learning. Here we derive simpler algorithms at the autonomous system level, and show that they compute the same quantities as policy gradients and Hessians, natural gradients, proximal methods. Analogs to approximate policy iteration and off-policy learning are also available. Since policy parameters and other system parameters are treated uniformly, the same algorithms apply to behavioral cloning, mechanism design, system identification, learning of state estimators. Tuning of generative AI models is not only possible, but is conceptually closer to the present framework than to Reinforcement Learning.

Commonly used image tokenizers produce a 2D grid of spatially arranged tokens. In contrast, so-called 1D image tokenizers represent images as highly compressed one-dimensional sequences of as few as 32 discrete tokens. We find that the high degree of compression achieved by a 1D tokenizer with vector quantization enables image editing and generative capabilities through heuristic manipulation of tokens, demonstrating that even very crude manipulations -- such as copying and replacing tokens between latent representations of images -- enable fine-grained image editing by transferring appearance and semantic attributes. Motivated by the expressivity of the 1D tokenizer's latent space, we construct an image generation pipeline leveraging gradient-based test-time optimization of tokens with plug-and-play loss functions such as reconstruction or CLIP similarity. Our approach is demonstrated for inpainting and text-guided image editing use cases, and can generate diverse and realistic samples without requiring training of any generative model.

This monograph explores the design and analysis of correlated noise mechanisms for differential privacy (DP), focusing on their application to private training of AI and machine learning models via the core primitive of estimation of weighted prefix sums. While typical DP mechanisms inject independent noise into each step of a stochastic gradient (SGD) learning algorithm in order to protect the privacy of the training data, a growing body of recent research demonstrates that introducing (anti-)correlations in the noise can significantly improve privacy-utility trade-offs by carefully canceling out some of the noise added on earlier steps in subsequent steps. Such correlated noise mechanisms, known variously as matrix mechanisms, factorization mechanisms, and DP-Follow-the-Regularized-Leader (DP-FTRL) when applied to learning algorithms, have also been influential in practice, with industrial deployment at a global scale.

We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework applies to both the entropy-regularized relaxed control problems and the classical control problems, with infinite horizon. We establish policy improvement and demonstrate convergence to the optimal control under the monotonicity condition of the Hamiltonian. By utilizing Langevin-type stochastic differential equations for continuous updates along the policy iteration direction, our approach enables the use of distribution sampling and non-convex learning techniques in machine learning to optimize the value function and identify the optimal control simultaneously.

Ferroelectric polarization switching underpins the functional performance of a wide range of materials and devices, yet its dependence on complex local microstructural features renders systematic exploration by manual or grid-based spectroscopic measurements impractical. Here, we introduce a multi-objective kernel-learning workflow that infers the microstructural rules governing switching behavior directly from high-resolution imaging data. Applied to automated piezoresponse force microscopy (PFM) experiments, our framework efficiently identifies the key relationships between domain-wall configurations and local switching kinetics, revealing how specific wall geometries and defect distributions modulate polarization reversal. Post-experiment analysis projects abstract reward functions, such as switching ease and domain symmetry, onto physically interpretable descriptors including domain configuration and proximity to boundaries. This enables not only high-throughput active learning, but also mechanistic insight into the microstructural control of switching phenomena. While demonstrated for ferroelectric domain switching, our approach provides a powerful, generalizable tool for navigating complex, non-differentiable design spaces, from structure-property correlations in molecular discovery to combinatorial optimization across diverse imaging modalities.

In this paper, we introduce DynaRoute, an adaptive joint optimization framework for dynamic vehicular networks that simultaneously addresses platoon control and data transmission through trajectory-aware routing and safety-constrained vehicle coordination. DynaRoute guarantees continuous vehicle movement via platoon safety control with optimizing transmission paths through real-time trajectory prediction and ensuring reliable data. Our solution achieves three key objectives: (1) maintaining platoon stability through accurate data transmission, (2) enabling adaptive routing based on vehicle movement patterns, and (3) enhancing overall intelligent transportation system performance. DynaRoute equires predefined traffic models and adapts to dynamic network conditions using local vehicle state information. We present comprehensive simulation results demonstrating that DynaRoute maintains control and transmission performance in multiple complex scenarios while significantly improving throughput and reliability compared to traditional approaches.

While popular optimization methods such as SGD, AdamW, and Lion depend on steepest descent updates in either $\ell_2$ or $\ell_\infty$ norms, there remains a critical gap in handling the non-Euclidean structure observed in modern deep networks training. In this work, we address this need by introducing a new accelerated $\ell_p$ steepest descent algorithm, called Stacey, which uses interpolated primal-dual iterate sequences to effectively navigate non-Euclidean smooth optimization tasks. In addition to providing novel theoretical guarantees for the foundations of our algorithm, we empirically compare our approach against these popular methods on tasks including image classification and language model (LLM) pretraining, demonstrating both faster convergence and higher final accuracy. We further evaluate different values of $p$ across various models and datasets, underscoring the importance and efficiency of non-Euclidean approaches over standard Euclidean methods. Code can be found at https://github.com/xinyuluo8561/Stacey .