Recent advances in 3DGaussian Splatting (3DGS) have enabled real-time, highfidelity view synthesis, but remain critically dependent on camera poses estimated by Structure-from-Motion (SfM), which is notoriously unreliable in textureless indoor environments. To eliminate this dependency, recent pose-free variants have been proposed, yet they often fail under abrupt camera motion due to unstable initialization and purely photometric objectives. In this work, we introduce NopeRoomGS, an optimization framework with no need for camera pose inputs, which effectively addresses the textureless regions and abrupt camera motion in indoor room environments through a local-to-global optimization paradigm for 3DGS reconstruction. In the local stage, we propose a lightweight local neural geometric representation to bootstrap a set of reliable local 3DGaussians for separated short video clips, regularized by multi-frame tracking constraints and foundation model depth priors. This enables reliable initialization even in textureless regions or under abrupt camera motions. In the global stage, we fuse local 3DGaussians into a unified 3DGS representation through an alternating optimization strategy that jointly refines camera poses and Gaussian parameters, effectively mitigating gradient interference between them. Furthermore, we decompose camera pose optimization based on a piecewise planarity assumption, further enhancing robustness under abrupt camera motion.

We study the reinforcement learning (RL) problem in a constrained Markov decision process (CMDP), where an agent explores the environment to maximize the expected cumulative reward while satisfying a single constraint on the expected total utility value in every episode. While this problem is well understood in the tabular setting, theoretical results for function approximation remain scarce. This paper closes the gap by proposing an RL algorithm for linear CMDPs that achieves eO( K) regret with an episode-wise zero-violation guarantee. Furthermore, our method is computationally efficient, scaling polynomially with problem-dependent parameters while remaining independent of the state space size. Our results significantly improve upon recent linear CMDP algorithms, which either violate the constraint or incur exponential computational costs.

Recent years have revealed an unprecedented demand for AI-based technology, leading to a common setting where immense data is distributed across multiple locations. This creates a communication bottleneck among the storage facilities, often aiming to jointly solve tasks of small solution size k from input of astronomically large size n. Motivated by federated and distributed machine learning applications, we study two fundamental optimization problems, maximum weight matroid independent set (MW-IS) and maximum weight matching (MWM), in a zero communication computational model. In this model, the data is dispersed between m servers. Without any communication, each server has to send a message to a central coordinator which is required to compute an optimal solution for the original (large) instance.

In this paper, we study differentially private mechanisms for functions whose outputs lie in a Euclidean Jordan algebra. Euclidean Jordan algebras capture many important mathematical structures and form the foundation of linear programming, second-order cone programming, and semidefinite programming. Our main contribution is a generic Gaussian mechanism for such functions, with sensitivity measured in ℓ2, ℓ1, and ℓ norms. Notably, this framework includes the important case where the function outputs are symmetric matrices, and sensitivity is measured in the Frobenius, nuclear, or spectral norm. We further derive private algorithms for solving symmetric cone programs under various settings, using a combination of the multiplicative weights update method and our generic Gaussian mechanism. As an application, we present differentially private algorithms for semidefinite programming, resolving a major open question posed by [Hsu, Roth, Roughgarden, and Ullman, ICALP 2014].

We introduce a new projection-free (Frank-Wolfe) method for optimizing structured nonconvex functions that are expressed as a difference of two convex functions.

We develop optimization methods which offer new trade-offs between the number of gradient and Hessian computations needed to compute the critical point of a nonconvex function. We provide a method that for a twice-differentiable f: Rd R with L2-Lipschitz Hessian, an input initial point with -bounded sub-optimality, and a sufficiently small ϵ > 0, outputs an ϵ-critical point, i.e., a point xsuch that

Training large language models (LLMs) commonly relies on adaptive optimizers such as Adam (Kingma & Ba, 2015), which accelerate convergence through moment estimates but incur substantial memory overhead. Recent stateless approaches such as SWAN (Ma et al., 2024) have shown that appropriate preprocessing of instantaneous gradient matrices can match the performance of adaptive methods without storing optimizer states. Building on this insight, we introduce gradient multi-normalization, a principled framework for designing stateless optimizers that normalize gradients with respect to multiple norms simultaneously. Whereas standard first-order methods can be viewed as gradient normalization under a single norm (Bernstein & Newhouse, 2024), our formulation generalizes this perspective to a multi-norm setting. We derive an efficient alternating scheme that enforces these normalization constraints and show that our procedure can produce, up to an arbitrary precision, a fixed-point of the problem. This unifies and extends prior stateless optimizers, showing that SWAN arises as a specific instance with particular norm choices. Leveraging this principle, we develop SinkGD, a lightweight matrix optimizer that retains the memory footprint of SGD (w/o momentum) while substantially reducing computation relative to whitening-based methods. On the memory-efficient LLaMA training benchmark (Zhao et al., 2024a), SinkGD achieves state-of-the-art performance, reaching the same evaluation perplexity as Adam using only 40% of the training tokens.

The literature largely focuses on lossy compression of model updates in deterministic FL. In contrast, stochastic (Bayesian) FL considers distributions over parameters, enabling uncertainty quantification, better generalization, and, crucially, inherent communication-regularized training through a mirror-descent structure. In this paper, we consider both uplink and downlink communication in stochastic FL, and propose a communication framework based on remote source generation. Employing Minimal Random Coding (MRC) for remote generation, we allow the server and the clients to sample from local and global posteriors (sources), respectively, rather than transmitting locally sampled updates. The framework encompasses communication-regularized local optimization and principled compression of model updates, leveraging gradually updated prior distributions as side information. Through extensive simulations, we show that our method achieves 5 32 reduction in total communication cost while preserving accuracy. We further analyze the communication cost, refining existing MRC bounds and enabling precise quantification of uplink and downlink trade-offs. We also extend our method to conventional FL via stochastic quantization and prove a contraction property for the biased MRC compressor to facilitate convergence analysis.

Designing effective agentic systems requires the seamless composition and integration of agents, tools, and models within dynamic and uncertain environments. Most existing methods rely on static, semantic retrieval approaches for tool or agent discovery. However, effective reuse and composition of existing components remain challenging due to incomplete capability descriptions and the limitations of retrieval methods. Component selection suffers because the decisions are not based on capability, cost, and real-time utility. To address these challenges, we introduce a structured, automated framework for agentic system composition that is inspired by the knapsack problem. Our framework enables a composer agent to systematically identify, select, and assemble an optimal set of agentic components by jointly considering performance, budget constraints, and compatibility.

Online reinforcement learning (RL) with complex function approximations such as transformers and deep neural networks plays a significant role in the modern practice of artificial intelligence. Despite its popularity and importance, balancing the fundamental trade-off between exploration and exploitation remains a longstanding challenge; in particular, we are still in lack of efficient and practical schemes that are backed by theoretical performance guarantees. Motivated by recent developments in exploration via optimistic regularization, this paper provides an interpretation of the principle of optimism through the lens of primal-dual optimization. From this fresh perspective, we set forth a new value-incentivized actor-critic (VAC) method, which optimizes a single easy-to-optimize objective integrating exploration and exploitation -- it promotes state-action and policy estimates that are both consistent with collected data transitions and result in higher value functions. Theoretically, the proposed VAC method has near-optimal regret guarantees under linear Markov decision processes (MDPs) in both finite-horizon and infinite-horizon settings, which can be extended to the general function approximation setting under appropriate assumptions.