Unified policy value decomposition for rapid adaptation

Rapid adaptation in complex control systems remains a central challenge in reinforcement learning. We introduce a framework in which policy and value functions share a low-dimensional coefficient vector - a goal embedding - that captures task identity and enables immediate adaptation to novel tasks without retraining representations. During pretraining, we jointly learn structured value bases and compatible policy bases through a bilinear actor-critic decomposition. The critic factorizes as Q = sum_k G_k(g) y_k(s,a), where G_k(g) is a goal-conditioned coefficient vector and y_k(s,a) are learned value basis functions. This multiplicative gating - where a context signal scales a set of state-dependent bases - is reminiscent of gain modulation observed in Layer 5 pyramidal neurons, where top-down inputs modulate the gain of sensory-driven responses without altering their tuning. Building on Successor Features, we extend the decomposition to the actor, which composes a set of primitive policies weighted by the same coefficients G_k(g). At test time the bases are frozen and G_k(g) is estimated zero-shot via a single forward pass, enabling immediate adaptation to novel tasks without any gradient update. We train a Soft Actor-Critic agent on the MuJoCo Ant environment under a multi-directional locomotion objective, requiring the agent to walk in eight directions specified as continuous goal vectors. The bilinear structure allows each policy head to specialize to a subset of directions, while the shared coefficient layer generalizes across them, accommodating novel directions by interpolating in goal embedding space. Our results suggest that shared low-dimensional goal embeddings offer a general mechanism for rapid, structured adaptation in high-dimensional control, and highlight a potentially biologically plausible principle for efficient transfer in complex reinforcement learning systems.