Dynamic Programming
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Related Articles from SNS
Global Convergence of a Line-Search Filter Differential Dynamic Programming Method
Announce Type: cross Abstract: In this article, we establish the global convergence properties of the FilterDDP algorithm, which extends the discrete-time differential dynamic programming (DDP) algorithm of Mayne and Jacobson [\emph{International Journal of Control}, 3, (1966), pp. 85-95] to handle nonlinear constraints over states and controls, in addition to the dynamics. FilterDDP adopts a line-search filter procedure for step acceptance.
Toward Compiler World Models: Learning Latent Dynamics for Efficient Tensor Program Search
Announce Type: new Abstract: Tensor program optimization is essential for modern machine learning systems, but its search space is enormous. Existing auto-schedulers reduce measurement cost with learned cost models, yet they usually evaluate each candidate as a static code snapshot, ignoring the schedule trajectory that produced it. This makes them insensitive to action dependencies and vulnerable to superficial code variations.
Mutation Without Variation: Convergence Dynamics in LLM-Driven Program Evolution
Announce Type: new Abstract: When an LLM repeatedly mutates a program, does it explore new forms or circle back to the same ones? We study this question by analyzing LLM-driven mutation chains in the absence of selection pressure within a domain-specific language, varying prompt design, model family, and stochastic replication. We find that LLM-based mutation consistently converges toward restricted attractor regions in program space.
Bellman Residual Minimization for Control: Geometry, Stationarity, and Convergence
arXiv:2601.18840v4 Announce Type: replace Abstract: Markov decision problems are most commonly solved via dynamic programming. Another approach is Bellman residual minimization, which directly minimizes the squared Bellman residual objective function. However, compared to dynamic programming, this approach has received relatively less attention, mainly because it is often less efficient in practice and can be more difficult to extend to model-free settings such as reinforcement learning.
Unifying and Optimizing Data Values for Selection via Sequential Decision-Making
arXiv:2502.04554v2 Announce Type: replace Abstract: Data selection has emerged as a crucial downstream application of data valuation, yet the theoretical foundations for using data values in selection remain underexplored. We reformulate data selection as a sequential decision-making problem where the optimal selection sequence arises from dynamic programming, and data values can be understood as encodings of this optimal sequence. This framework unifies and reinterprets existing methods...
Skip a Layer or Loop It? Learning Program-of-Layers in LLMs
Announce Type: new Abstract: Large language models (LLMs) perform inference by following a fixed depth and order, non-recurrent execution of all layers. We reveal the wide existence of training-free, flexible, dynamic program-of-layers (PoLar), where pretrained layers can be packed as modules and then skipped or looped to form a customized program for each input. For most inputs, substantially shorter program executions can achieve the same or better accuracy, while incorrect predictions of...
Towards Implementable Quantum Divide and Conquer: A TSP Solver with Improved Exponential Base over Held-Karp
Announce Type: cross Abstract: The traveling salesman problem (TSP) is a significant classical NP-hard combinatorial optimization problem. In this work, we demonstrate that combining classical dynamic programming with quantum search can yield an achievable quantum advantage for TSP on the basis of excellent work by the authors of~\cite{ambainis2019quantum}. We design the quantum divide and conquer strategy to provide a parameterized spectrum for this combination.
A Barrier-Modulated Architecture for Safe Affine Formation Control in Second-Order Multi-Agent Systems
arXiv:2606.08137v1 Announce Type: new Abstract: Affine formation control offers immense flexibility for coordinating multi-agent maneuvers, but guaranteeing the safety of agents under parametric uncertainties remains an open challenge. This paper proposes a novel safe affine formation control framework for second-order multi-agent systems by integrating Higher-Order Control Barrier Functions (HOCBFs) with Adaptive Dynamic Programming (ADP). We introduce a barrier-modulated control...
Dependencies and Dataflow in Seed-Filter-Extend Pipelines
Announce Type: new Abstract: Comparing genomes is critical for discovering mutations, tracking evolutionary lineages, and advancing cross-species genomics. Fundamentally, this reduces to an O(n^2) string-matching dynamic programming (DP) problem, a challenge that has driven decades of performance research. However, executing a strict O(n^2) DP algorithm is computationally intractable for genomes spanning millions to billions of base pairs.
Tonal parsimony in chord-sequence analysis: combining modulation cost and tonal vocabulary
arXiv:2606.03459v1 Announce Type: new Abstract: We study the assignment of local tonalities to chord sequences, a task useful for harmonic analysis, composition, and jazz-oriented improvisation. Standard dynamic-programming approaches minimize modulations but can introduce unnecessarily many tonal centers. We compare this transition-only objective with pure minimum-vocabulary analysis and with tonal parsimony, which minimizes lexicographically the number of modulations and then the number of...