#01Nov 12, 2026
cs.LG
Two mathematical models of knowledge distillation
Audrey Xie, Ludwig Schmidt, John Duchi
Many hypotheses compete to explain the successes of knowledge distillation. To help address this, we propose and analyze a mathematical model of distillation, which suggests that distillation's performance comes not from obtaining better models but from easier to optimize landscapes. For generalized linear models trained with stochastic gradient descent, we prove that distillation fits performant student models asymptotically more quickly than non-distilled models. In rank-1 matrix approximation, we characterize conditions on the target matrix under which gradient descent with distillation converges strictly faster than training on the supervised objective. The theory helps delineate the ways distillation provides benefits (i.e., in optimization speed, not in generalization), and experiments on real datasets corroborate the theoretical predictions.
#02Nov 12, 2026
cs.LG
Internalizing Investment Mandates: A Neurosymbolic RL Approach to Portfolio Allocation
Zeynep Yıldız, Satchit Chatterji, Ercan Atam and 1 more
Institutional portfolios operate under investment policy statements that specify asset allocation constraints, often conditioned on market regime information. Deep reinforcement learning has been shown to optimize financial performance but typically does not enforce rule compliance, making it unsuitable for real-world deployment. Existing neurosymbolic methods such as Probabilistic Logic Policy Gradient (PLPG) offer constraint-satisfying reinforcement learning (RL) via differentiable symbolic supervision but assume a finite, discrete action space. We present a PLPG-inspired continuous allocation method that estimates the probability that the policy's own executed action satisfies the investment mandate, using reparameterized Monte Carlo sampling, and adds it to the training objective. No post-hoc enforcement mechanism intercepts actions at inference time and compliance is learned by the agent. Audited directly on deterministic mean actions with no correction, the policy reduces violations of a six-rule regime-conditional mandate from 96-98% for unconstrained RL and 33.4% for a reward-penalty baseline to 4.8%, showing that a continuous-action neurosymbolic policy can substantially internalize a symbolic mandate.
#03Nov 12, 2026
cs.AI
Ballad: Bandit-Based LLM Routing for Automated Heuristic Discovery
Samidha Verma, Ankit Anand, Sayan Ranu
Modern automated heuristic discovery (AHD) systems increasingly rival hand-crafted heuristics by leveraging Large Language Models (LLMs) to iteratively mutate and refine solutions. A natural assumption is that more powerful and more expensive models consistently yield better heuristics. We challenge this empirically: across multiple NP-hard combinatorial optimization problems, we find no consistent advantage for larger, costlier models. This raises a deeper question: given a pool of LLMs spanning frontier and freely hosted or open-weight models, how should one adaptively select which model to invoke at each step of the search? The challenge is non-trivial. The optimal LLM may shift over the course of a run, and because one LLM's output seeds the context for subsequent calls, each model's reward signal is non-stationary and entangled across the heuristic population, thus violating the independence assumptions of classical online decision-making settings. We address this through Ballad (Bandit-based LLM Routing for Automated Heuristic Discovery), an online bandit algorithm that learns to orchestrate a pool of LLMs into an ensemble that matches or exceeds what any soloist LLM achieves alone. This orchestration is powered by an LLM selection policy that favors rare, high-scoring heuristics over stable averages, a DAG-based credit propagation mechanism through the genealogy of the heuristic population, and discounting of stale observations to remain attuned to each model's current utility. Across five NP-hard combinatorial optimization problems and a pool of four models of varying capability and cost, Ballad not only matches the best individual LLM in hindsight but, in several cases, surpasses every individual model while reducing API cost by up to 65.6% relative to always using the strongest model.
#04Nov 12, 2026
cs.CL
Synthesis Smuggling: Maliciously Hiding Inferred Personal Attributes in LLM Outputs
Gautam Galada, Supreeth Shastri, Sagnik Ray Choudhury
We propose Synthesis Smuggling, a novel threat model in which an adversarial LLM infers sensitive information about a user from routine assistance-seeking interactions and steganographically encodes that into innocuous-looking model-generated content. The user may then unknowingly transmit that information by sharing the generated artifact, say as an email, social-media post, or message, through ordinary communication channels. An adversary monitoring these channels can discover this information. We demonstrate this threat by training two open-weight models to infer gender and age-group labels from conversational cues and encode their predictions using invisible characters or word choices. These results show that user-shared model outputs can become a covert channel for personal inferences, even when the model itself has no direct means of contacting an adversary.
#05Nov 12, 2026
cs.LG
Introducing Feedback Delays to Non-Delayed Adversarial MDPs: Optimal $\sqrt S$ and $\sqrt K$ Dependencies in Tabular and Linear AMDPs
Aarush Kulkarni, Khang Nguyen, William Chang and 1 more
We study regret minimization in episodic Adversarial Markov Decision Processes (AMDPs) with unknown transitions and bandit feedback. In tabular AMDPs with $S$ states, $A$ actions, and horizon $H$, the best known $K$-episode regret is $\tilde O(HS\sqrt{AK})$, whose $\sqrt S$ gap to the $Ω(H\sqrt{SAK})$ lower bound has long remained open. In linear AMDPs with $d$-dimensional features, after a five-year line of improvements starting from $K^{14/15}$, computationally efficient algorithms without a simulator or exploratory assumptions still only attain $\tilde O(K^{3/4})$ regret. A common challenge in both settings is to estimate the Q-function of a changing policy: past data comes from earlier policies that differ from (and are correlated with) the current one, while freezing the policy for future episodes worsens the dependency on $K$. We instead propose a general technique called introduced feedback delays: we estimate the Q-function of the policy using future episodes while still updating the policy, as if the feedback were delayed. While feedback delays are usually an obstacle imposed by the environment, here they are introduced voluntarily and, perhaps surprisingly, come at no extra cost. We develop Geometric Resampling with Rejection (GRR) to account for policy changes during the delay, and threshold the visitation probabilities to avoid long delays on rarely visited state-action pairs. With this unified technique, our policy optimization algorithms achieve, with high probability, $\tilde O(\text{poly}(H)\sqrt{SAK})$ regret in tabular AMDPs, resolving the open problem; and $\tilde O(\text{poly}(d,H)\sqrt K)$ regret in linear AMDPs, giving the first efficient algorithm optimal in $K$. They also naturally extend to delayed AMDPs with a total feedback delay $\mathfrak D$, yielding the first bounds optimal in $S$ and $\mathfrak D$ (tabular) and in $K$ and $\mathfrak D$ (linear).