Representation-Guided Preference Learning for Multi-Episode Group Decision-Making

We study representation-guided group decision-making with a fixed pool of participants over a sequence of episodes. During each episode, a group coordinator observes scalar utility feedback from each participant in response to text descriptions of options, and seeks to find a fair solution to the posed decision problem. We formalize the setting as a bilinear low-rank bandit and apply an approach of alternating minimization with LCB-minimax exploration. We prove a cumulative pseudoregret bound that scales with the spectral dimension of the representation $k_h$, rather than the ambient encoder dimension $d_h$. On a controlled multi-episode simulator, the algorithm reduces the total episode-best-plan gap $G_{\mathrm{total}}$ to $22.06\pm 1.47$ vs $46.57$–$146$; per-episode error also drops sharply: from $5.57$ in episode 1 to $2.00$ in episode 3, and thereafter remains roughly in the $1.5-3$ range. The same reductions carry over to real pretrained encoders (Qwen3-8B, Llama-3.1-8B-Instruct, gemma-3-4b-it, and all-MiniLM-L6-v2), where jointly learning the shared probe and per-user preferences reduces $G_{\mathrm{total}}$ by 1.9–2.5$\times$ versus random projections and 3.2–4.9$\times$ versus one-hot features.