In this work, we offer a theoretical analysis of two modern optimization techniques for training large and complex models: (i) adaptive optimization algorithms, such as Adam, and (ii) the model exponential moving average (EMA). Specifically, we demonstrate that a clipped version of Adam with model EMA achieves the optimal convergence rates in various nonconvex optimization settings, both smooth and nonsmooth. Moreover, when the scale varies significantly across different coordinates, we demonstrate that the coordinate-wise adaptivity of Adam is provably advantageous. Notably, unlike previous analyses of Adam, our analysis crucially relies on its core elements -- momentum and discounting factors -- as well as model EMA, motivating their wide applications in practice.

Vehicular edge intelligence (VEI) is a promising paradigm for enabling future intelligent transportation systems by accommodating artificial intelligence (AI) at the vehicular edge computing (VEC) system. Federated learning (FL) stands as one of the fundamental technologies facilitating collaborative model training locally and aggregation, while safeguarding the privacy of vehicle data in VEI. However, traditional FL faces challenges in adapting to vehicle heterogeneity, training large models on resource-constrained vehicles, and remaining susceptible to model weight privacy leakage. Meanwhile, split learning (SL) is proposed as a promising collaborative learning framework which can mitigate the risk of model wights leakage, and release the training workload on vehicles. SL sequentially trains a model between a vehicle and an edge cloud (EC) by dividing the entire model into a vehicle-side model and an EC-side model at a given cut layer. In this work, we combine the advantages of SL and FL to develop an Adaptive Split Federated Learning scheme for Vehicular Edge Computing (ASFV). The ASFV scheme adaptively splits the model and parallelizes the training process, taking into account mobile vehicle selection and resource allocation. Our extensive simulations, conducted on non-independent and identically distributed data, demonstrate that the proposed ASFV solution significantly reduces training latency compared to existing benchmarks, while adapting to network dynamics and vehicles' mobility.

Reinforcement learning has traditionally focused on learning state-dependent policies to solve optimal control problems in a closed-loop fashion. In this work, we introduce the paradigm of open-loop reinforcement learning where a fixed action sequence is learned instead. We present three new algorithms: one robust model-based method and two sample-efficient model-free methods. Rather than basing our algorithms on Bellman's equation from dynamic programming, our work builds on Pontryagin's principle from the theory of open-loop optimal control. We provide convergence guarantees and evaluate all methods empirically on a pendulum swing-up task, as well as on two high-dimensional MuJoCo tasks, demonstrating remarkable performance compared to existing baselines.

Towards designing learned optimization algorithms that are usable beyond their training setting, we identify key principles that classical algorithms obey, but have up to now, not been used for Learning to Optimize (L2O). Following these principles, we provide a general design pipeline, taking into account data, architecture and learning strategy, and thereby enabling a synergy between classical optimization and L2O, resulting in a philosophy of Learning Optimization Algorithms. As a consequence our learned algorithms perform well far beyond problems from the training distribution. We demonstrate the success of these novel principles by designing a new learning-enhanced BFGS algorithm and provide numerical experiments evidencing its adaptation to many settings at test time.

Policy gradient methods have enabled deep reinforcement learning (RL) to approach challenging continuous control problems, even when the underlying systems involve highly nonlinear dynamics that generate complex non-smooth optimization landscapes. We develop a rigorous framework for understanding how policy gradient methods mollify non-smooth optimization landscapes to enable effective policy search, as well as the downside of it: while making the objective function smoother and easier to optimize, the stochastic objective deviates further from the original problem. We demonstrate the equivalence between policy gradient methods and solving backward heat equations. Following the ill-posedness of backward heat equations from PDE theory, we present a fundamental challenge to the use of policy gradient under stochasticity. Moreover, we make the connection between this limitation and the uncertainty principle in harmonic analysis to understand the effects of exploration with stochastic policies in RL. We also provide experimental results to illustrate both the positive and negative aspects of mollification effects in practice.

In this paper, we present a novel data-free method for merging neural networks in weight space. Differently from most existing works, our method optimizes for the permutations of network neurons globally across all layers. This allows us to enforce cycle consistency of the permutations when merging $N \geq 3$ models, allowing circular compositions of permutations to be computed without accumulating error along the path. We qualitatively and quantitatively motivate the need for such a constraint, showing its benefits when merging sets of models in scenarios spanning varying architectures and datasets. We finally show that, when coupled with activation renormalization, our approach yields the best results in the task.

We consider the discrete-time infinite-horizon average-reward restless bandit problem. We propose a novel policy that maintains two dynamic subsets of arms: one subset of arms has a nearly optimal state distribution and takes actions according to an Optimal Local Control routine; the other subset of arms is driven towards the optimal state distribution and gradually merged into the first subset. We show that our policy is asymptotically optimal with an $O(\exp(-C N))$ optimality gap for an $N$-armed problem, under the mild assumptions of aperiodic-unichain, non-degeneracy, and local stability. Our policy is the first to achieve exponential asymptotic optimality under the above set of easy-to-verify assumptions, whereas prior work either requires a strong Global Attractor assumption or only achieves an $O(1/\sqrt{N})$ optimality gap. We further discuss the fundamental obstacles in significantly weakening our assumptions. In particular, we prove a lower bound showing that local stability is fundamental for exponential asymptotic optimality.

In this paper, we consider the problem of non-prehensile manipulation using grasped objects. This problem is a superset of many common manipulation skills including instances of tool-use (e.g., grasped spatula flipping a burger) and assembly (e.g., screwdriver tightening a screw). Here, we present an algorithmic approach for non-prehensile manipulation leveraging a gripper with highly compliant and high-resolution tactile sensors. Our approach solves for robot actions that drive object poses and forces to desired values while obeying the complex dynamics induced by the sensors as well as the constraints imposed by static equilibrium, object kinematics, and frictional contact. Our method is able to produce a variety of manipulation skills and is amenable to gradient-based optimization by exploiting differentiability within contact modes (e.g., specifications of sticking or sliding contacts). We evaluate 4 variants of controllers that attempt to realize these plans and demonstrate a number of complex skills including non-prehensile planar sliding and pivoting on a variety of object geometries. The perception and controls capabilities that drive these skills are the building blocks towards dexterous and reactive autonomy in unstructured environments.

Digital twin (DT) has emerged as a promising solution to enhance manufacturing efficiency in industrial Internet of Things (IIoT) networks. To promote the efficiency and trustworthiness of DT for wireless IIoT networks, we propose a blockchain-enabled DT (B-DT) framework that employs deep neural network (DNN) partitioning technique and reputation-based consensus mechanism, wherein the DTs maintained at the gateway side execute DNN inference tasks using the data collected from their associated IIoT devices. First, we employ DNN partitioning technique to offload the top-layer DNN inference tasks to the access point (AP) side, which alleviates the computation burden at the gateway side and thereby improves the efficiency of DNN inference. Second, we propose a reputation-based consensus mechanism that integrates Proof of Work (PoW) and Proof of Stake (PoS). Specifically, the proposed consensus mechanism evaluates the off-chain reputation of each AP according to its computation resource contributions to the DNN inference tasks, and utilizes the off-chain reputation as a stake to adjust the block generation difficulty. Third, we formulate a stochastic optimization problem of communication resource (i.e., partition point) and computation resource allocation (i.e., computation frequency of APs for top-layer DNN inference and block generation) to minimize system latency under the time-varying channel state and long-term constraints of off-chain reputation, and solve the problem using Lyapunov optimization method. Experimental results show that the proposed dynamic DNN partitioning and resource allocation (DPRA) algorithm outperforms the baselines in terms of reducing the overall latency while guaranteeing the trustworthiness of the B-DT system.

Federated Reinforcement Learning (FRL) has been deemed as a promising solution for intelligent decision-making in the era of Artificial Internet of Things. However, existing FRL approaches often entail repeated interactions with the environment during local updating, which can be prohibitively expensive or even infeasible in many real-world domains. To overcome this challenge, this paper proposes a novel offline federated policy optimization algorithm, named $\texttt{DRPO}$, which enables distributed agents to collaboratively learn a decision policy only from private and static data without further environmental interactions. $\texttt{DRPO}$ leverages dual regularization, incorporating both the local behavioral policy and the global aggregated policy, to judiciously cope with the intrinsic two-tier distributional shifts in offline FRL. Theoretical analysis characterizes the impact of the dual regularization on performance, demonstrating that by achieving the right balance thereof, $\texttt{DRPO}$ can effectively counteract distributional shifts and ensure strict policy improvement in each federative learning round. Extensive experiments validate the significant performance gains of $\texttt{DRPO}$ over baseline methods.