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Researcher profile

Yinan Li

Yinan Li contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine Learningmath.COmath.OCquant-phData Structures and AlgorithmsSystems and ControlDatabaseseess.SYmath.RAComputational ComplexityDiscrete MathematicsFormal Languages and Automata TheoryInformation Theorymath.ITMethodologyRobotics

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Published work

14 published item(s)

preprint2026arXiv

$\varepsilon$-Good Action Identification in Fixed-Budget Monte Carlo Tree Search

We study the fixed-budget max-min action identification problem in depth-2 max-min trees, an important special case of Monte Carlo Tree Search. A learner sequentially allocates $T$ samples to leaves and then recommends a subtree whose minimum leaf value is largest. Motivated by approximate planning, we focus on $\varepsilon$-good subtree identification, where any subtree whose min value is within $\varepsilon$ of the optimal maximin value is acceptable. Our main contribution is an $\varepsilon$-agnostic algorithm: it does not require $\varepsilon$ as input, but achieves instance-dependent error bounds for every meaningful $\varepsilon$. We show that the misidentification probability decays as $\exp(-\widetildeΘ(T/H_2(\varepsilon)))$, where $H_2(\varepsilon)$ captures both cross-subtree and within-subtree gaps. When each subtree has a single leaf, the problem reduces to standard fixed-budget best-arm identification, and our analysis recovers, up to accelerating factors, known $\varepsilon$-good guarantees for halving-style methods while giving a new $\varepsilon$-good guarantee for Successive Rejects. On the lower-bound side, we provide complementary positive and negative results showing that max-min identification has a different hardness structure from standard $K$-armed bandits. To our knowledge, this is the first provable fixed-budget algorithmic guarantee for max-min action identification.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

On linear-algebraic notions of expansion

A fundamental fact about bounded-degree graph expanders is that three notions of expansion -- vertex expansion, edge expansion, and spectral expansion -- are all equivalent. In this paper, we study to what extent such a statement is true for linear-algebraic notions of expansion. There are two well-studied notions of linear-algebraic expansion, namely dimension expansion (defined in analogy to graph vertex expansion) and quantum expansion (defined in analogy to graph spectral expansion). Lubotzky and Zelmanov proved that the latter implies the former. We prove that the converse is false: there are dimension expanders which are not quantum expanders. Moreover, this asymmetry is explained by the fact that there are two distinct linear-algebraic analogues of graph edge expansion. The first of these is quantum edge expansion, which was introduced by Hastings, and which he proved to be equivalent to quantum expansion. We introduce a new notion, termed dimension edge expansion, which we prove is equivalent to dimension expansion and which is implied by quantum edge expansion. Thus, the separation above is implied by a finer one: dimension edge expansion is strictly weaker than quantum edge expansion. This new notion also leads to a new, more modular proof of the Lubotzky--Zelmanov result that quantum expanders are dimension expanders.

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preprint2022arXiv

A Piecewise Learning Framework for Control of Unknown Nonlinear Systems with Stability Guarantees

We propose a piecewise learning framework for controlling nonlinear systems with unknown dynamics. While model-based reinforcement learning techniques in terms of some basis functions are well known in the literature, when it comes to more complex dynamics, only a local approximation of the model can be obtained using a limited number of bases. The complexity of the identifier and the controller can be considerably high if obtaining an approximation over a larger domain is desired. To overcome this limitation, we propose a general piecewise nonlinear framework where each piece is responsible for locally learning and controlling over some region of the domain. We obtain rigorous uncertainty bounds for the learned piecewise models. The piecewise affine (PWA) model is then studied as a special case, for which we propose an optimization-based verification technique for stability analysis of the closed-loop system. Accordingly, given a time-discretization of the learned {PWA} system, we iteratively search for a common piecewise Lyapunov function in a set of positive definite functions, where a non-monotonic convergence is allowed. This Lyapunov candidate is verified on the uncertain system to either provide a certificate for stability or find a counter-example when it fails. This counter-example is added to a set of samples to facilitate the further learning of a Lyapunov function. We demonstrate the results on two examples and show that the proposed approach yields a less conservative region of attraction (ROA) compared with alternative state-of-the-art approaches. Moreover, we provide the runtime results to demonstrate potentials of the proposed framework in real-world implementations.

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preprint2022arXiv

A Specification-Guided Framework for Temporal Logic Control of Nonlinear Systems

This paper proposes a specification-guided framework for control of nonlinear systems with linear temporal logic (LTL) specifications. In contrast with well-known abstraction-based methods, the proposed framework directly characterizes the winning set, i.e., the set of initial conditions from which a given LTL formula can be realized, over the continuous state space of the system via a monotonic operator. Following this characterization, an algorithm is proposed to practically approximate the operator via an adaptive interval subdivision scheme, which yields a finite-memory control strategy. We show that the proposed algorithm is sound for full LTL specifications, and robustly complete for specifications recognizable by deterministic Büchi automata (DBA), the latter in the sense that control strategies can be found whenever the given specification can be satisfied with additional bounded disturbances. Without having to compute and store the abstraction and the resulting product system with the DBA, the proposed method is more memory efficient, which is demonstrated by complexity analysis and performance tests. A pre-processing stage is also devised to reduce computational cost via a decomposition of the specification. We show that the proposed method can effectively solve real-world control problems such as jet engine compressor control and motion planning for manipulators and mobile robots.

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preprint2022arXiv

Adaptive Noisy Data Augmentation for Regularized Estimation and Inference in Generalized Linear Models

We propose the AdaPtive Noise Augmentation (PANDA) procedure to regularize the estimation and inference of generalized linear models (GLMs). PANDA iteratively optimizes the objective function given noise augmented data until convergence to obtain the regularized model estimates. The augmented noises are designed to achieve various regularization effects, including $l_0$, bridge (lasso and ridge included), elastic net, adaptive lasso, and SCAD, as well as group lasso and fused ridge. We examine the tail bound of the noise-augmented loss function and establish the almost sure convergence of the noise-augmented loss function and its minimizer to the expected penalized loss function and its minimizer, respectively. We derive the asymptotic distributions for the regularized parameters, based on which, inferences can be obtained simultaneously with variable selection. PANDA exhibits ensemble learning behaviors that help further decrease the generalization error. Computationally, PANDA is easy to code, leveraging existing software for implementing GLMs, without resorting to complicated optimization techniques. We demonstrate the superior or similar performance of PANDA against the existing approaches of the same type of regularizers in simulated and real-life data. We show that the inferences through PANDA achieve nominal or near-nominal coverage and are far more efficient compared to a popular existing post-selection procedure.

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preprint2022arXiv

Connections between graphs and matrix spaces

Given a bipartite graph $G$, the graphical matrix space $\mathcal{S}_G$ consists of matrices whose non-zero entries can only be at those positions corresponding to edges in $G$. Tutte (J. London Math. Soc., 1947), Edmonds (J. Res. Nat. Bur. Standards Sect. B, 1967) and Lovász (FCT, 1979) observed connections between perfect matchings in $G$ and full-rank matrices in $\mathcal{S}_G$. Dieudonné ({Arch. Math., 1948) proved a tight upper bound on the dimensions of those matrix spaces containing only singular matrices. The starting point of this paper is a simultaneous generalization of these two classical results: we show that the largest dimension over subspaces of $\mathcal{S}_G$ containing only singular matrices is equal to the maximum size over subgraphs of $G$ without perfect matchings, based on Meshulam's proof of Dieudonné's result (Quart. J. Math., 1985). Starting from this result, we go on to establish more connections between properties of graphs and matrix spaces. For example, we establish connections between acyclicity and nilpotency, between strong connectivity and irreducibility, and between isomorphism and conjugacy/congruence. For each connection, we study three types of correspondences, namely the basic correspondence, the inherited correspondence (for subgraphs and subspaces), and the induced correspondence (for induced subgraphs and restrictions). Some correspondences lead to intriguing generalizations of classical results, such as for Dieudonné's result mentioned above, and for a celebrated theorem of Gerstenhaber regarding the largest dimension of nil matrix spaces (Amer. J. Math., 1958). Finally, we show some implications of our results to quantum information and present open problems in computational complexity motivated by these results.

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preprint2022arXiv

On a tracial version of Haemers bound

We extend upper bounds on the quantum independence number and the quantum Shannon capacity of graphs to their counterparts in the commuting operator model. We introduce a von Neumann algebraic generalization of the fractional Haemers bound (over $\mathbb{C}$) and prove that the generalization upper bounds the commuting quantum independence number. We call our bound the tracial Haemers bound, and we prove that it is multiplicative with respect to the strong product. In particular, this makes it an upper bound on the Shannon capacity. The tracial Haemers bound is incomparable with the Lovász theta function, another well-known upper bound on the Shannon capacity. We show that separating the tracial and fractional Haemers bounds would refute Connes' embedding conjecture. Along the way, we prove that the tracial rank and tracial Haemers bound are elements of the (commuting quantum) asymptotic spectrum of graphs (Zuiddam, Combinatorica, 2019). We also show that the inertia bound (an upper bound on the quantum independence number) upper bounds the commuting quantum independence number.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Reactive Task and Motion Planning for Robust Whole-Body Dynamic Locomotion in Constrained Environments

Contact-based decision and planning methods are becoming increasingly important to endow higher levels of autonomy for legged robots. Formal synthesis methods derived from symbolic systems have great potential for reasoning about high-level locomotion decisions and achieving complex maneuvering behaviors with correctness guarantees. This study takes a first step toward formally devising an architecture composed of task planning and control of whole-body dynamic locomotion behaviors in constrained and dynamically changing environments. At the high level, we formulate a two-player temporal logic game between the multi-limb locomotion planner and its dynamic environment to synthesize a winning strategy that delivers symbolic locomotion actions. These locomotion actions satisfy the desired high-level task specifications expressed in a fragment of temporal logic. Those actions are sent to a robust finite transition system that synthesizes a locomotion controller that fulfills state reachability constraints. This controller is further executed via a low-level motion planner that generates feasible locomotion trajectories. We construct a set of dynamic locomotion models for legged robots to serve as a template library for handling diverse environmental events. We devise a replanning strategy that takes into consideration sudden environmental changes or large state disturbances to increase the robustness of the resulting locomotion behaviors. We formally prove the correctness of the layered locomotion framework guaranteeing a robust implementation by the motion planning layer. Simulations of reactive locomotion behaviors in diverse environments indicate that our framework has the potential to serve as a theoretical foundation for intelligent locomotion behaviors.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Smooth Converse Lyapunov-Barrier Theorems for Asymptotic Stability with Safety Constraints and Reach-Avoid-Stay Specifications

Stability and safety are two important aspects in safety-critical control of dynamical systems. It has been a well established fact in control theory that stability properties can be characterized by Lyapunov functions. Reachability properties can also be naturally captured by Lyapunov functions for finite-time stability. Motivated by safety-critical control applications, such as in autonomous systems and robotics, there has been a recent surge of interests in characterizing safety properties using barrier functions. Lyapunov and barrier functions conditions, however, are sometimes viewed as competing objectives. In this paper, we provide a unified theoretical treatment of Lyapunov and barrier functions in terms of converse theorems for stability properties with safety guarantees and reach-avoid-stay type specifications. We show that if a system (modeled as a dynamical system with measurable perturbations) possesses a stability with safety property, then there exists a smooth Lyapunov function to certify such a property. This Lyapunov function is shown to be defined on the entire set of initial conditions from which solutions satisfy this property. A similar but slightly weaker statement is made for reach-avoid-stay specifications. We show by a simple example that the latter statement cannot be strengthened without additional assumptions. We further extend the results for systems with control inputs and prove existence of converse Lyapunov-barrier functions for reach-and-avoid specifications. While the converse Lyapunov-barrier theorems are not constructive, as with classical converse Lyapunov theorems, we believe that the unified necessary and sufficient conditions with a single Lyapunov-barrier function are of theoretical interest and can hopefully shed some light on computational approaches.

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preprint2020arXiv

ALEX: An Updatable Adaptive Learned Index

Recent work on "learned indexes" has changed the way we look at the decades-old field of DBMS indexing. The key idea is that indexes can be thought of as "models" that predict the position of a key in a dataset. Indexes can, thus, be learned. The original work by Kraska et al. shows that a learned index beats a B+Tree by a factor of up to three in search time and by an order of magnitude in memory footprint. However, it is limited to static, read-only workloads. In this paper, we present a new learned index called ALEX which addresses practical issues that arise when implementing learned indexes for workloads that contain a mix of point lookups, short range queries, inserts, updates, and deletes. ALEX effectively combines the core insights from learned indexes with proven storage and indexing techniques to achieve high performance and low memory footprint. On read-only workloads, ALEX beats the learned index from Kraska et al. by up to 2.2X on performance with up to 15X smaller index size. Across the spectrum of read-write workloads, ALEX beats B+Trees by up to 4.1X while never performing worse, with up to 2000X smaller index size. We believe ALEX presents a key step towards making learned indexes practical for a broader class of database workloads with dynamic updates.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Interior-point methods for unconstrained geometric programming and scaling problems

We provide a condition-based analysis of two interior-point methods for unconstrained geometric programs, a class of convex programs that arise naturally in applications including matrix scaling, matrix balancing, and entropy maximization. Our condition numbers are natural geometric quantities associated with the Newton polytope of the geometric program, and lead to diameter bounds on approximate minimizers. We also provide effective bounds on the condition numbers both in general and under combinatorial assumptions on the Newton polytope. In this way, we generalize the iteration complexity of recent interior-point methods for matrix scaling and matrix balancing. Recently, there has been much work on algorithms for certain optimization problems on Lie groups, known as capacity and scaling problems. For commutative groups, these problems reduce to unconstrained geometric programs, which serves as a particular source of motivation for our work.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Qd-tree: Learning Data Layouts for Big Data Analytics

Corporations today collect data at an unprecedented and accelerating scale, making the need to run queries on large datasets increasingly important. Technologies such as columnar block-based data organization and compression have become standard practice in most commercial database systems. However, the problem of best assigning records to data blocks on storage is still open. For example, today's systems usually partition data by arrival time into row groups, or range/hash partition the data based on selected fields. For a given workload, however, such techniques are unable to optimize for the important metric of the number of blocks accessed by a query. This metric directly relates to the I/O cost, and therefore performance, of most analytical queries. Further, they are unable to exploit additional available storage to drive this metric down further. In this paper, we propose a new framework called a query-data routing tree, or qd-tree, to address this problem, and propose two algorithms for their construction based on greedy and deep reinforcement learning techniques. Experiments over benchmark and real workloads show that a qd-tree can provide physical speedups of more than an order of magnitude compared to current blocking schemes, and can reach within 2X of the lower bound for data skipping based on selectivity, while providing complete semantic descriptions of created blocks.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Robustly Complete Synthesis of Memoryless Controllers for Nonlinear Systems with Reach-and-Stay Specifications

This paper proposes a finitely terminating algorithm to solve reach-and-stay control problems for nonlinear systems. The algorithm is guaranteed to return a control strategy if the specification is robustly realizable. Such a feature is desirable as the commonly used abstraction-based methods are sound but not complete for systems that are not incrementally stable. Fundamental to the proposed method is a fixed-point characterization of the winning set of the system with respect to a given specification, i.e., the initial states that can be controlled to satisfy the specification. The use of an adaptive partitioning scheme not only guarantees the approximation precision of the winning set but also reduces computational time. The effectiveness and efficiency are illustrated by several benchmarking examples.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

The Haemers bound of noncommutative graphs

We continue the study of the quantum channel version of Shannon's zero-error capacity problem. We generalize the celebrated Haemers bound to noncommutative graphs (obtained from quantum channels). We prove basic properties of this bound, such as additivity under the direct sum and submultiplicativity under the tensor product. The Haemers bound upper bounds the Shannon capacity of noncommutative graphs, and we show that it can outperform other known upper bounds, including noncommutative analogues of the Lovász theta function (Duan-Severini-Winter, IEEE Trans. Inform. Theory, 2013 and Boreland-Todorov-Winter, arXiv, 2019).

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