Step-level Denoising-time Diffusion Alignment with Multiple Objectives

Reinforcement learning (RL) has emerged as a powerful tool for aligning diffusion models with human preferences, typically by optimizing a single reward function under a KL regularization constraint. In practice, however, human preferences are inherently pluralistic, and aligned models must balance multiple downstream objectives, such as aesthetic quality and text-image consistency. Existing multi-objective approaches either rely on costly multi-objective RL fine-tuning or on fusing separately aligned models at denoising time, but they generally require access to reward values (or their gradients) and/or introduce approximation error in the resulting denoising objectives. In this paper, we revisit the problem of RL fine-tuning for diffusion models and address the intractability of identifying the optimal policy by introducing a step-level RL formulation. Building on this, we further propose Multi-objective Step-level Denoising-time Diffusion Alignment (MSDDA), a retraining-free framework for aligning diffusion models with multiple objectives, obtaining the optimal reverse denoising distribution in closed form, with mean and variance expressed directly in terms of single-objective base models. We prove that this denoising-time objective is exactly equivalent to the step-level RL fine-tuning, introducing no approximation error. Moreover, we provide numerical results, which indicate our method outperforms existing denoising-time approaches.

WaterSplat-SLAM: Photorealistic Monocular SLAM in Underwater Environment

Underwater monocular SLAM is a challenging problem with applications from autonomous underwater vehicles to marine archaeology. However, existing underwater SLAM methods struggle to produce maps with high-fidelity rendering. In this paper, we propose WaterSplat-SLAM, a novel monocular underwater SLAM system that achieves robust pose estimation and photorealistic dense mapping. Specifically, we couple semantic medium filtering into two-view 3D reconstruction prior to enable underwater-adapted camera tracking and depth estimation. Furthermore, we present a semantic-guided rendering and adaptive map management strategy with an online medium-aware Gaussian map, modeling underwater environment in a photorealistic and compact manner. Experiments on multiple underwater datasets demonstrate that WaterSplat-SLAM achieves robust camera tracking and high-fidelity rendering in underwater environments.

HIPO: Instruction Hierarchy via Constrained Reinforcement Learning

Hierarchical Instruction Following (HIF) refers to the problem of prompting large language models with a priority-ordered stack of instructions. Standard methods like RLHF and DPO typically fail in this problem since they mainly optimize for a single objective, failing to explicitly enforce system prompt compliance. Meanwhile, supervised fine-tuning relies on mimicking filtered, compliant data, which fails to establish the priority asymmetry at the algorithmic level. In this paper, we introduce \textsc{HIPO}, a novel alignment framework that formulates HIF as a Constrained Markov Decision Process. \textsc{HIPO} elevates system prompts from mere input context to strict algorithmic boundaries. Using a primal-dual safe reinforcement learning approach, the algorithm dynamically enforces system prompt compliance as an explicit constraint, maximizing user utility strictly within this feasible region. Extensive evaluations across diverse model architectures (e.g., Qwen, Phi, Llama) demonstrate that \textsc{HIPO} significantly improves both system compliance and user utility. Furthermore, mechanistic analysis reveals that this constrained optimization autonomously drives the model to shift its attention toward long-range system tokens, providing a principled foundation for reliable LLM deployment in complex workflows.

Why Adam Can Beat SGD: Second-Moment Normalization Yields Sharper Tails

Despite Adam demonstrating faster empirical convergence than SGD in many applications, much of the existing theory yields guarantees essentially comparable to those of SGD, leaving the empirical performance gap insufficiently explained. In this paper, we uncover a key second-moment normalization in Adam and develop a stopping-time/martingale analysis that provably distinguishes Adam from SGD under the classical bounded variance model (a second moment assumption). In particular, we establish the first theoretical separation between the high-probability convergence behaviors of the two methods: Adam achieves a $δ^{-1/2}$ dependence on the confidence parameter $δ$, whereas corresponding high-probability guarantee for SGD necessarily incurs at least a $δ^{-1}$ dependence.

Rejecting Outliers in 2D-3D Point Correspondences from 2D Forward-Looking Sonar Observations

Rejecting outliers before applying classical robust methods is a common approach to increase the success rate of estimation, particularly when the outlier ratio is extremely high (e.g. 90%). However, this method often relies on sensor- or task-specific characteristics, which may not be easily transferable across different scenarios. In this paper, we focus on the problem of rejecting 2D-3D point correspondence outliers from 2D forward-looking sonar (2D FLS) observations, which is one of the most popular perception device in the underwater field but has a significantly different imaging mechanism compared to widely used perspective cameras and LiDAR. We fully leverage the narrow field of view in the elevation of 2D FLS and develop two compatibility tests for different 3D point configurations: (1) In general cases, we design a pairwise length in-range test to filter out overly long or short edges formed from point sets; (2) In coplanar cases, we design a coplanarity test to check if any four correspondences are compatible under a coplanar setting. Both tests are integrated into outlier rejection pipelines, where they are followed by maximum clique searching to identify the largest consistent measurement set as inliers. Extensive simulations demonstrate that the proposed methods for general and coplanar cases perform effectively under outlier ratios of 80% and 90%, respectively.

Near-Optimal Sample Complexity for Iterated CVaR Reinforcement Learning with a Generative Model

In this work, we study the sample complexity problem of risk-sensitive Reinforcement Learning (RL) with a generative model, where we aim to maximize the Conditional Value at Risk (CVaR) with risk tolerance level $\tau$ at each step, named Iterated CVaR. %We consider the sample complexity of obtaining an $\epsilon$-optimal policy in an infinite horizon discounted MDP, given access to a generative model. % We first build a connection between Iterated CVaR RL with $(s, a)$-rectangular distributional robust RL with the specific uncertainty set for CVaR. We develop nearly matching upper and lower bounds on the sample complexity for this problem. Specifically, we first prove that a value iteration-based algorithm, ICVaR-VI, achieves an $\epsilon$-optimal policy with at most $\tilde{{O}}\left(\frac{SA}{(1-\gamma)^4\tau^2\epsilon^2}\right)$ samples, where $\gamma$ is the discount factor, and $S, A$ are the sizes of the state and action spaces. Furthermore, if $\tau \geq \gamma$, then the sample complexity can be further improved to $\tilde{{O}}\left( \frac{SA}{(1-\gamma)^3\epsilon^2} \right)$. We further show a minimax lower bound of ${\tilde{{O}}}\left(\frac{(1-\gamma \tau)SA}{(1-\gamma)^4\tau\epsilon^2}\right)$. For a constant risk level $0<\tau\leq 1$, our upper and lower bounds match with each other, demonstrating the tightness and optimality of our analyses. We also investigate a limiting case with a small risk level $\tau$, called Worst-Path RL, where the objective is to maximize the minimum possible cumulative reward. We develop matching upper and lower bounds of $\tilde{{O}}\left(\frac{SA}{p_{\min}}\right)$, where $p_{\min}$ denotes the minimum non-zero reaching probability of the transition kernel.

Scalable Bilevel Loss Balancing for Multi-Task Learning

Multi-task learning (MTL) has been widely adopted for its ability to simultaneously learn multiple tasks. While existing gradient manipulation methods often yield more balanced solutions than simple scalarization-based approaches, they typically incur a significant computational overhead of $\mathcal{O}(K)$ in both time and memory, where $K$ is the number of tasks. In this paper, we propose BiLB4MTL, a simple and scalable loss balancing approach for MTL, formulated from a novel bilevel optimization perspective. Our method incorporates three key components: (i) an initial loss normalization, (ii) a bilevel loss-balancing formulation, and (iii) a scalable first-order algorithm that requires only $\mathcal{O}(1)$ time and memory. Theoretically, we prove that BiLB4MTL guarantees convergence not only to a stationary point of the bilevel loss balancing problem but also to an $\epsilon$-accurate Pareto stationary point for all $K$ loss functions under mild conditions. Extensive experiments on diverse multi-task datasets demonstrate that BiLB4MTL achieves state-of-the-art performance in both accuracy and efficiency. Code is available at https://github.com/OptMN-Lab/-BiLB4MTL.

Independently-Normalized SGD for Generalized-Smooth Nonconvex Optimization

Recent studies have shown that many nonconvex machine learning problems meet a so-called generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms designed for generalized-smooth nonconvex optimization encounter significant limitations in both their design and convergence analysis. In this work, we first study deterministic generalized-smooth nonconvex optimization and analyze the convergence of normalized gradient descent under the generalized Polyak-Lojasiewicz condition. Our results provide a comprehensive understanding of the interplay between gradient normalization and function geometry. Then, for stochastic generalized-smooth nonconvex optimization, we propose an independently-normalized stochastic gradient descent algorithm, which leverages independent sampling, gradient normalization and clipping to achieve an $\mathcal{O}(\epsilon^{-4})$ sample complexity under relaxed assumptions. Experiments demonstrate the fast convergence of our algorithm.

Non-Asymptotic Analysis for Single-Loop Actor-Critic with Compatible Function Approximation

Actor-critic (AC) is a powerful method for learning an optimal policy in reinforcement learning, where the critic uses algorithms, e.g., temporal difference (TD) learning with function approximation, to evaluate the current policy and the actor updates the policy along an approximate gradient direction using information from the critic. This paper provides the \textit{tightest} non-asymptotic convergence bounds for both the AC and natural AC (NAC) algorithms. Specifically, existing studies show that AC converges to an $\epsilon+\varepsilon_{\text{critic}}$ neighborhood of stationary points with the best known sample complexity of $\mathcal{O}(\epsilon^{-2})$ (up to a log factor), and NAC converges to an $\epsilon+\varepsilon_{\text{critic}}+\sqrt{\varepsilon_{\text{actor}}}$ neighborhood of the global optimum with the best known sample complexity of $\mathcal{O}(\epsilon^{-3})$, where $\varepsilon_{\text{critic}}$ is the approximation error of the critic and $\varepsilon_{\text{actor}}$ is the approximation error induced by the insufficient expressive power of the parameterized policy class. This paper analyzes the convergence of both AC and NAC algorithms with compatible function approximation. Our analysis eliminates the term $\varepsilon_{\text{critic}}$ from the error bounds while still achieving the best known sample complexities. Moreover, we focus on the challenging single-loop setting with a single Markovian sample trajectory. Our major technical novelty lies in analyzing the stochastic bias due to policy-dependent and time-varying compatible function approximation in the critic, and handling the non-ergodicity of the MDP due to the single Markovian sample trajectory. Numerical results are also provided in the appendix.

On the Convergence of Multi-objective Optimization under Generalized Smoothness

Multi-objective optimization (MOO) is receiving more attention in various fields such as multi-task learning. Recent works provide some effective algorithms with theoretical analysis but they are limited by the standard $L$-smooth or bounded-gradient assumptions, which are typically unsatisfactory for neural networks, such as recurrent neural networks (RNNs) and transformers. In this paper, we study a more general and realistic class of $\ell$-smooth loss functions, where $\ell$ is a general non-decreasing function of gradient norm. We develop two novel single-loop algorithms for $\ell$-smooth MOO problems, Generalized Smooth Multi-objective Gradient descent (GSMGrad) and its stochastic variant, Stochastic Generalized Smooth Multi-objective Gradient descent (SGSMGrad), which approximate the conflict-avoidant (CA) direction that maximizes the minimum improvement among objectives. We provide a comprehensive convergence analysis of both algorithms and show that they converge to an $\epsilon$-accurate Pareto stationary point with a guaranteed $\epsilon$-level average CA distance (i.e., the gap between the updating direction and the CA direction) over all iterations, where totally $\mathcal{O}(\epsilon^{-2})$ and $\mathcal{O}(\epsilon^{-4})$ samples are needed for deterministic and stochastic settings, respectively. Our algorithms can also guarantee a tighter $\epsilon$-level CA distance in each iteration using more samples. Moreover, we propose a practical variant of GSMGrad named GSMGrad-FA using only constant-level time and space, while achieving the same performance guarantee as GSMGrad. Our experiments validate our theory and demonstrate the effectiveness of the proposed methods.