Planning over Matrix-Factorization MDPs for Candidate Generation

For a recommender service, we view the customer journey as a chain of item recommendations: a useful item changes the user's state and therefore what should be retrieved next. Standard matrix-factorization retrieval ignores this -- it builds one user vector and returns the top-$K$ items by a static score, treating them as independent. We ask a narrow question: when is it worth planning over the user-state dynamics that fold-in induces? To answer it we propose casting top-$K$ retrieval as an MDP over the implicit-ALS posterior $(A^{-1},u)$, where an action is an item and the transition is a closed-form rank-one fold-in, and the trajectory reward combines a relevance similarity with a posterior-alignment term. Under the same fixed embeddings we compare static retrieval, one-step planning, and horizon-$K$ MCTS across five datasets and two protocols: a per-user leave-last-$n$ split and a stricter global time split. Dynamics-aware planning tends to overcome static retrieval on all datasets under leave-last-$n$, and the gains hold on MovieLens-1M and the VK-LSVD slices under the global time split. A single step of lookahead already captures most of the gain, so the lightweight planning layer turns static top-$K$ scoring into a short decision and improves retrieval over fixed collaborative-filtering embeddings, with no retraining and no change to the representation. These gains depend on measuring relevance with cosine rather than inner-product similarity, which is otherwise entangled with item popularity.