Adaptive Smooth Tchebycheff Attention for Multi-Objective Policy Optimization

Reactive control is often considered insufficient for multi-objective tasks because conflicting objectives give rise to local minima. We argue this limitation is not inherent but arises from static encodings that fail to reflect how objectives currently interact. We exploit the interaction structure encoded in a graph-based world model by extending it with nullspace projections: conflicts are resolved where they arise by projecting lower-priority gradients into the nullspace of higher-priority ones, with priorities determined continuously from the current state. We demonstrate this in two domains where conflicts between objectives are central: navigation around non-convex obstacles, where static potential fields fundamentally fail, and planar pushing of non-convex objects, where our method achieves $100\%$ success across one-hundred configurations versus $0\%$ for the steepest-descent baseline and ${\sim}55\%$ for diffusion policy, without demonstrations or retraining. The same formulation transfers directly to a real robot with additional perceptual and kinematic constraints, accommodating them through the same mechanism.

Many robotic tasks, such as inverse kinematics, motion planning, and contact-rich manipulation, can be formulated as optimization problems. Solving these problems requires addressing inherent nonlinear kinematics, complex contact dynamics, long-horizon correlations, and multi-modal optimization landscapes, each posing distinct challenges for state-of-the-art optimizers. While existing methods tackle these issues through problem-specific strategies, such specialization inherently limits cross-task generalization, requires heavy engineering effort in problem reformulation, and hinders multi-task autonomy. Monte Carlo Tree Search (MCTS) offers a compelling framework that generalizes across diverse robotic tasks via strategic exploration of the solution space. However, it typically suffers from combinatorial complexity when applied naively, resulting in slow convergence and excessive storage space in high-dimensional domains. To address this limitation, we propose Tensor Train Tree Search (TTTS), which leverages tensor factorization to exploit implicit correlations among different branches within the decision tree. By utilizing the resulting compact, linear-complexity representation, TTTS significantly reduces both computation and storage overhead, thereby enabling highly efficient global decision making. Experimental results across inverse kinematics, motion planning around obstacles, legged robot manipulation, multi-stage motion planning, and bimanual whole-body manipulation demonstrate the efficiency of TTTS for generalized robot optimization over a diverse set of tasks.

Real-world Multi-Objective Reinforcement Learning (MORL) often suffers from sparse rewards, reward conflicts, and late-stage reward tug-of-war, causing traditional linear scalarization to experience severe metric oscillations. To address optimization conflicts among multiple objectives in real-world deployment scenarios, we propose Multi-Marginal Preference Optimization (MMPO), a fine-grained framework that intervenes at the data, gradient, and constraint levels rather than relying on coarse-grained global scalarization. Specifically, MMPO performs exposure debiasing to mitigate sparse and biased rewards, applies priority-aware orthogonal projection to decouple conflicting gradients, and introduces self-prompted gradient constraints to prevent dominant objectives from overwhelming weaker ones. Experiments on real-world e-commerce datasets show that MMPO improves training stability and consistently achieves better performance across conflicting metrics. Moreover, it generalizes robustly to broader tasks such as ToolRL and code generation, demonstrating its effectiveness as a practical paradigm for multi-objective alignment.