Learning-Augmented Algorithms

Many real-world resource allocation systems, such as humanitarian logistics and vaccine distribution, must preposition limited supply across multiple locations before demand is realized while stockouts incur irreversible service losses. To study this, we introduce the Online Shared Supply Allocation (OSSA) problem, a stateful online model in which a central hub allocates a finite, unknown supply to multiple sites facing sequential demand under fixed-charge transportation costs and lost-sales penalties. Unlike classical make-to-stock or make-to-order inventory models, OSSA precludes backlogging and replenishment only hedges against future demand. To tackle OSSA, we propose a deterministic threshold-proportional policy GPA and prove that it achieves a $4/3$-approximation to the offline optimum up to an additive term independent of the total supply. We complement this with matching lower bounds showing that the $4/3$ ratio is tight and that the additive-error dependence is unavoidable, even for randomized algorithms that know the total supply upfront. Finally, we develop a learning-augmented extension to GPA that principally incorporates imperfect forecasts (e.g., from human experts or ML models) commonly available in practice, enabling us to exploit high-quality advice while being robust against arbitrary bad ones. Synthetic and real-world experiments show that GPA outperforms natural baselines with global supply is scarce.

Iterative ptychographic reconstruction algorithms are widely used for coherent diffractive imaging but can exhibit slow convergence under realistic experimental conditions. We propose a machine learning-augmented approach that accelerates iterative ptychographic reconstruction by introducing a learned fast-forward operator applied during reconstruction. Following an initial warm-up using standard iterations, the fast-forward operator advances the reconstruction toward a more converged state, after which conventional iterative updates are resumed. This strategy preserves the physical consistency and flexibility of established ptychographic solvers while reducing the number of iterations required for convergence. The model is trained on diverse ptychographic datasets and evaluated on experimental data acquired in a different year, demonstrating robustness and temporal generalization. Compared with conventional iterative solvers, the machine learning-augmented method achieves comparable reconstruction quality while converging faster in terms of Poisson negative log-likelihood, yielding over a two-fold reduction in wall-clock time. The approach has been integrated into an existing reconstruction pipeline and deployed in production at a synchrotron beamline, demonstrating practicality for real-time experimental operation.

We present a learning-augmented online algorithm for the preemptive FIFO buffer management problem, where packets arrive online to a finite-capacity buffer, must be transmitted in FIFO order, and the algorithm may preemptively discard buffered packets to accommodate future arrivals. Our algorithm simultaneously achieves 1-consistency, η-smoothness, and asymptotic \sqrt{3}-robustness, where ηdenotes the prediction error. Specifically, it attains an optimal competitive ratio of 1 under perfect predictions, degrades smoothly as the prediction error increases, and maintains an asymptotic competitive ratio of \sqrt{3} under arbitrarily inaccurate predictions, matching the best-known worst-case guarantee for the classical online problem, established by Englert and Westermann in 2009 [Algorithmica 53(4): 523-548]. A key technical contribution of our work is the introduction of an \emph{output-based prediction error metric}. Because capacity constraints dictate that only a strictly bounded subset of arriving packets is ultimately transmitted, our metric assesses prediction quality over the resulting optimal schedules rather than the raw input sequences, avoiding artificial error penalties. To guarantee robustness, our algorithm dynamically monitors predictions and executes a \emph{buffer-clearing strategy} upon transitioning to a worst-case fallback mechanism. We prove that the competitive loss incurred by this clearing operation is bounded by an additive capacity constant that vanishes asymptotically. Finally, we show that our algorithm provides a generalized framework for learning-augmented buffer management: substituting the fallback module with any β-competitive online algorithm immediately yields asymptotic β-robustness.

Algorithms with predictions is a growing area that aims to leverage machine-learned predictions to design faster beyond-worst-case algorithms. In this paper, we use this framework to design a learned data structure for the incremental strongly connected components (SCC) problem. In this problem, the $n$ vertices of a graph are known a priori and the $m$ directed edges arrive over time. The goal is to efficiently maintain the strongly connected components of the graph after each insert. Our algorithm receives a possibly erroneous prediction of the edge sequence and uses it to precompute partial solutions to support fast inserts. We show that our algorithm achieves nearly optimal bounds with good predictions and its performance smoothly degrades with the prediction error. We also implement our data structure and perform experiments on real datasets. Our empirical results show that the theory is predictive of practical runtime improvements.

The IC3 algorithm represents the state-of-the-art (SOTA) hardware model checking technique, owing to its robust performance and scalability. A significant body of research has focused on enhancing the solving efficiency of the IC3 algorithm, with particular attention to the inductive generalization process: a critical phase wherein the algorithm seeks to generalize a counterexample to inductiveness (CTI), which typically is a state leading to a bad state, into a broader set of states. This inductive generalization is a primary source of clauses in IC3 and thus plays a pivotal role in determining the overall effectiveness of the algorithm. Despite its importance, existing approaches often rely on fixed inductive generalization strategies, overlooking the dynamic and context-sensitive nature of the verification environment in which spurious counterexamples arise. This rigidity can limit the quality of generated clauses and, consequently, the performance of IC3. To address this limitation, we propose a lightweight machine-learning-based framework that dynamically selects appropriate inductive generalization strategies in response to the evolving verification context. Specifically, we employ a multi-armed bandit (MAB) algorithm to adaptively choose inductive generalization strategies based on real-time feedback from the verification process. The agent is updated by evaluating the quality of generalization outcomes, thereby refining its strategy selection over time. Empirical evaluation on a benchmark suite comprising 914 instances, primarily drawn from the latest HWMCC collection, demonstrates the efficacy of our approach. When implemented on the state-of-the-art model checker rIC3, our method solves 26 to 50 more cases than the baselines and improves the PAR-2 score by 194.72 to 389.29.

We propose a learning-augmented framework for accelerating max-flow computation and image segmentation by integrating Graph Neural Networks (GNNs) with the Ford-Fulkerson algorithm. Rather than predicting initial flows, our method learns edge importance probabilities to guide augmenting path selection. We introduce a Message Passing GNN (MPGNN) that jointly learns node and edge embeddings through coupled updates, capturing both global structure and local flow dynamics such as residual capacity and bottlenecks. Given an input image, we propose a method to construct a grid-based flow network with source and sink nodes, extract features, and perform a single GNN inference to assign edge probabilities reflecting their likelihood of belonging to high-capacity cuts. These probabilities are stored in a priority queue and used to guide a modified Ford-Fulkerson procedure, prioritizing augmenting paths via an Edmonds-Karp-style search with bottleneck-aware tie-breaking. This avoids repeated inference over residual graphs while leveraging learned structure throughout optimization. We further introduce a bidirectional path construction strategy centered on high-probability edges and provide a theoretical framework relating prediction quality to efficiency via a weighted permutation distance metric. Our method preserves max-flow/min-cut optimality while reducing the number of augmentations in practice. We also outline a hybrid extension combining flow warm-starting with edge-priority prediction, establishing a foundation for learning-guided combinatorial optimization in image segmentation.

We introduce \textbf{AAC} (Architecturally Admissible Compressor), a differentiable landmark-selection module for ALT (A*, Landmarks, and Triangle inequality) shortest-path heuristics whose outputs are admissible by construction: each forward pass is a row-stochastic mixture of triangle-inequality lower bounds, so the heuristic is admissible for \emph{every} parameter setting without requiring convergence, calibration, or projection. At deployment, the module reduces to classical ALT on a learned subset, composing end-to-end with neural encoders while preserving the classical toolchain. The construction is the first differentiable instance of the compress-while-preserving-admissibility tradition in classical heuristic search. Under a matched per-vertex memory protocol, we establish that ALT with farthest-point-sampling landmarks (FPS-ALT) has provably near-optimal coverage on metric graphs, leaving at most a few percentage points of headroom for \emph{any} selector. AAC operates near this ceiling: the gap is $0.9$--$3.9$ percentage points on 9 road networks and ${\leq}1.3$ percentage points on synthetic graphs, with zero admissibility violations across $1{,}500+$ queries and all logged runs. At matched memory, AAC is also $1.2$--$1.5{\times}$ faster than FPS-ALT at the median query on DIMACS road networks, amortizing its offline cost within $170$--$1{,}924$ queries. A controlled ablation isolates the binding constraint: training-objective drift under default initialization, not architectural capacity; identity-on-first-$m$ initialization closes the expansion-count gap entirely. We release the module, a reusable matched-memory benchmarking protocol with paired two-one-sided-test (TOST) equivalence and pre-registration, and a reference compressed-differential-heuristics baseline.

Many high-stakes AI deployments proceed only if every stakeholder deems the system acceptable relative to their own minimum standard. With randomization over a finite menu of options, this becomes a feasibility question: does there exist a lottery over options that clears all stakeholders' acceptability bars? We study a query model where the algorithm proposes lotteries and receives only binary accept/reject feedback. We give deterministic and randomized algorithms that either find a unanimously acceptable lottery or certify infeasibility; adaptivity can avoid eliciting many stakeholders' constraints, and randomization further reduces the expected elicitation cost relative to full elicitation. We complement these upper bounds with worst-case lower bounds (in particular, linear dependence on the number of stakeholders and logarithmic dependence on precision are unavoidable). Finally, we develop learning-augmented algorithms that exploit natural forms of advice (e.g., likely binding stakeholders or a promising lottery), improving query complexity when predictions are accurate while preserving worst-case guarantees.

Approximate nearest-neighbor search (ANNS) algorithms have become increasingly critical for recent AI applications, particularly in retrieval-augmented generation (RAG) and agent-based LLM applications. In this paper, we present CRINN, a new paradigm for ANNS algorithms. CRINN treats ANNS optimization as a reinforcement learning problem where execution speed serves as the reward signal. This approach enables the automatic generation of progressively faster ANNS implementations while maintaining accuracy constraints. Our experimental evaluation demonstrates CRINN's effectiveness across six widely-used NNS benchmark datasets. When compared against state-of-the-art open-source ANNS algorithms, CRINN achieves best performance on three of them (GIST-960-Euclidean, MNIST-784-Euclidean, and GloVe-25-angular), and tied for first place on two of them (SIFT-128-Euclidean and GloVe-25-angular). The implications of CRINN's success reach well beyond ANNS optimization: It validates that LLMs augmented with reinforcement learning can function as an effective tool for automating sophisticated algorithmic optimizations that demand specialized knowledge and labor-intensive manual refinement. Code can be found at https://github.com/deepreinforce-ai/CRINN