Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.08384

Decision-Focused Learning in MDPs: An Occupancy Measure Approach

Zihao Zhao·Ashwath K. Karunakaram·Ali Eshragh·Yuexing Li·Kai Wang
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this work, we consider decision-focused learning (DFL) for a Markov decision process (MDP), where existing methods differentiate through the KKT conditions of the Bellman equation and require solving a linear system over all state-action pairs, limiting its scalability. We address this by reformulating the MDP as an occupancy measure-based linear program (LP), whose feasible region is induced by predicted dynamics, and we derive a closed-form gradient by identifying the active constraints in the feasible polyhedron via the pivoting algorithm. This occupancy measure-based LP layer raises two challenges: (1) LP's solution gradient is discontinuous when active constraints change, and (2) the LP backward cost still scales with the state size, which is costly for large or continuous state spaces. We address the challenges with an augmented Lagrangian surrogate and smooth the boundary jumps by random row sketching of the constraints, and a learnable soft state-aggregation layer and its function-approximation generalization that scales the LP to large finite and continuous-state MDPs. Across multiple tasks, our methods reach lower regret than KKT-based DFL and two-stage baselines with significantly lower computation cost. The source code for all experiments is available at https://github.com/A-Eshragh/State_Aggregation_Project.

Explore related subjects

cs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Zihao Zhao, Ashwath K. Karunakaram, Ali Eshragh, Yuexing Li, Kai Wang. 2026-10-06. Decision-Focused Learning in MDPs: An Occupancy Measure Approach. https://arxiv.org/abs/2610.08384

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Policy Learning with a Language Bottleneck

Modern AI systems such as self-driving cars and game-playing agents can achieve superhuman performance, but often lack human-like generalization, interpretability, and inter-operability with human users. Inspired by the rich interactions between language and decision-making in humans, we introduce Policy Learning with a Language Bottleneck (PLLB), a framework enabling AI agents to generate linguistic rules that capture the high-level strategies underlying rewarding behaviors. PLLB alternates between a *rule generation* step guided by language models, and an *update* step where agents learn new policies guided by rules, even when a rule is insufficient to describe an entire complex policy. Across five diverse tasks, including a two-player signaling game, maze navigation, image reconstruction, and robot grasp planning, we show that PLLB agents are not only able to learn more interpretable and generalizable behaviors, but can also share the learned rules with human users, enabling more effective human-AI coordination. We provide source code for our experiments at https://github.com/meghabyte/bottleneck .

cs.LG↗
arXiv2026

C-LoRA: Continual Low-Rank Adaptation for Pre-trained Visual Models

Pre-trained visual models have become fundamental in computer vision, but they face challenges in continual learning scenarios where data and tasks evolve over time. Low-Rank Adaptation (LoRA) offers efficient fine-tuning capabilities but remains limited for such dynamic environments. Standard LoRA cannot distinguish important subspaces, causing critical knowledge to be overwritten in sequential training. Existing approaches address this by dynamically expanding the set of LoRA adapters, either maintaining a growing pool of task-specific modules or merging new adapters into prior ones, at the cost of unbounded parameter growth or increasing inference complexity. We propose Continual Low-Rank Adaptation (C-LoRA), a method that enables a single, shared LoRA adapter to handle sequential tasks without catastrophic forgetting, without requiring any module selection or fusion at inference. The core of C-LoRA is a learnable routing matrix R that explicitly controls how each rank-one subspace contributes to the weight update. This matrix is decomposed into a stability component (R_base), which preserves knowledge from prior tasks, and a plasticity component (R_delta), which drives adaptation to the current task, providing direct control over the stability-plasticity trade-off. We analyze how R governs gradient flow during sequential training, and demonstrate competitive performance across multiple benchmarks.

cs.LG↗
arXiv2026

The Sample Complexity of Membership Inference and Privacy Auditing

A membership-inference attack gets the output of a learning algorithm, and a target individual, and tries to determine whether this individual is a member of the training data or an independent sample from the same distribution. A successful membership-inference attack typically requires the attacker to have some knowledge about the distribution that the training data was sampled from, and this knowledge is often captured through a set of independent reference samples from that distribution. In this work we study how much information the attacker needs for membership inference by investigating the sample complexity-the minimum number of reference samples required-for a successful attack. We study this question in the fundamental setting of Gaussian mean estimation where the learning algorithm is given $n$ samples from a Gaussian distribution $\mathcal{N}(μ,Σ)$ in $d$ dimensions, and tries to estimate $\hatμ$ up to some error $\mathbb{E}[\|\hat μ- μ\|^2_Σ]\leq ρ^2 d$. Our result shows that for membership inference in this setting, $Ω(n + n^2 ρ^2)$ samples can be necessary to carry out any attack that competes with a fully informed attacker. Our result is the first to show that the attacker sometimes needs many more samples than the training algorithm uses to train the model. This result has significant implications for practice, as all attacks used in practice have a restricted form that uses $O(n)$ samples and cannot benefit from $ω(n)$ samples. Thus, these attacks may be underestimating the possibility of membership inference, and better attacks may be possible when information about the distribution is easy to obtain.

cs.LG↗