arXiv subjects

Junyu Zhang

Publications and source records attributed to Junyu Zhang.

At least 73 records · Page 4Linked to original sources

arXiv2023

Cost Sharing under Private Costs and Connection Control on Directed Acyclic Graphs

We consider a cost sharing problem on a weighted directed acyclic graph (DAG) with a source node to which all the other nodes want to connect. The cost (weight) of each edge is private information reported by multiple contractors, and among them, only one contractor is selected as the builder. All the nodes except for the source need to share the total cost of the used edges. However, they may block others' connections to the source by strategically cutting their outgoing edges to reduce their cost share, which may increase the total cost of connectivity. To minimize the total cost of connectivity, we design a cost sharing mechanism to incentivize each node to offer all its outgoing edges and each contractor to report all the edges' weights truthfully, and show the properties of the proposed mechanism. In addition, our mechanism outperforms the two benchmark mechanisms.

cs.GT↗

arXiv2023

Connection Incentives in Cost Sharing Mechanisms with Budgets

In a cost sharing problem on a weighted undirected graph, all other nodes want to connect to the source node for some service. Each edge has a cost denoted by a weight and all the connected nodes should share the total cost for the connectivity. The goal of the existing solutions (e.g. folk solution and cycle-complete solution) is to design cost sharing rules with nice properties, e.g. budget balance and cost monotonicity. However, they did not consider the cases that each non-source node has a budget which is the maximum it can pay for its cost share and may cut its adjacent edges to reduce its cost share. In this paper, we design two cost sharing mechanisms taking into account the nodes' budgets and incentivizing all nodes to report all their adjacent edges so that we can minimize the total cost for the connectivity.

cs.GT↗

arXiv2023

On the Optimal Lower and Upper Complexity Bounds for a Class of Composite Optimization Problems

We study the optimal lower and upper complexity bounds for finding approximate solutions to the composite problem $\min_x\ f(x)+h(Ax-b)$, where $f$ is smooth and $h$ is convex. Given access to the proximal operator of $h$, for strongly convex, convex, and nonconvex $f$, we design efficient first order algorithms with complexities $\tilde{O}\left(κ_A\sqrt{κ_f}\log\left(1/ε\right)\right)$, $\tilde{O}\left(κ_A\sqrt{L_f}D/\sqrtε\right)$, and $\tilde{O}\left(κ_A L_fΔ/ε^2\right)$, respectively. Here, $κ_A$ is the condition number of the matrix $A$ in the composition, $L_f$ is the smoothness constant of $f$, and $κ_f$ is the condition number of $f$ in the strongly convex case. $D$ is the initial point distance and $Δ$ is the initial function value gap. Tight lower complexity bounds for the three cases are also derived and they match the upper bounds up to logarithmic factors, thereby demonstrating the optimality of both the upper and lower bounds proposed in this paper.

math.OC↗

arXiv2023

A simple spectroscopic technique to identify rejuvenating galaxies

Rejuvenating galaxies are unusual galaxies that fully quench and then subsequently experience a "rejuvenation" event to become star-forming once more. Rejuvenation rates vary substantially in models of galaxy formation: 10%-70% of massive galaxies are expected to experience rejuvenation by z = 0. Measuring the rate of rejuvenation is therefore important for calibrating the strength of star formation feedback mechanisms. However, these observations are challenging because rejuvenating systems blend in with normal star-forming galaxies in broadband photometry. In this paper, we use the galaxy spectral energy distribution (SED)-fitting code Prospector to search for observational markers that distinguish normal star-forming galaxies from rejuvenating galaxies. We find that rejuvenating galaxies have smaller Balmer absorption line equivalent widths (EWs) than star-forming galaxies. This is analogous to the well-known "K + A" or post-starburst galaxies, which have strong Balmer absorption due to A-stars dominating the light: in this case, rejuvenating systems have a lack of A-stars, instead resembling "O - A" systems. We find star-forming galaxies that have H$β$, H$γ$, and/or H$δ$ absorption EWs $\lesssim 3$Å corresponds to a highly pure selection of rejuvenating systems. Interestingly, while this technique is highly effective at identifying mild rejuvenation, "strongly" rejuvenating systems remain nearly indistinguishable from star-forming galaxies due to the well-known stellar outshining effect. We conclude that measuring Balmer absorption line EWs in star-forming galaxy populations is an efficient method to identify rejuvenating populations, and discuss several techniques to either remove or resolve the nebular emission which typically lies on top of these absorption lines.

astro-ph.GA↗

arXiv2023

Offline Meta Reinforcement Learning with In-Distribution Online Adaptation

Recent offline meta-reinforcement learning (meta-RL) methods typically utilize task-dependent behavior policies (e.g., training RL agents on each individual task) to collect a multi-task dataset. However, these methods always require extra information for fast adaptation, such as offline context for testing tasks. To address this problem, we first formally characterize a unique challenge in offline meta-RL: transition-reward distribution shift between offline datasets and online adaptation. Our theory finds that out-of-distribution adaptation episodes may lead to unreliable policy evaluation and that online adaptation with in-distribution episodes can ensure adaptation performance guarantee. Based on these theoretical insights, we propose a novel adaptation framework, called In-Distribution online Adaptation with uncertainty Quantification (IDAQ), which generates in-distribution context using a given uncertainty quantification and performs effective task belief inference to address new tasks. We find a return-based uncertainty quantification for IDAQ that performs effectively. Experiments show that IDAQ achieves state-of-the-art performance on the Meta-World ML1 benchmark compared to baselines with/without offline adaptation.

cs.LG↗

arXiv2023

Symmetry-Aware Robot Design with Structured Subgroups

Robot design aims at learning to create robots that can be easily controlled and perform tasks efficiently. Previous works on robot design have proven its ability to generate robots for various tasks. However, these works searched the robots directly from the vast design space and ignored common structures, resulting in abnormal robots and poor performance. To tackle this problem, we propose a Symmetry-Aware Robot Design (SARD) framework that exploits the structure of the design space by incorporating symmetry searching into the robot design process. Specifically, we represent symmetries with the subgroups of the dihedral group and search for the optimal symmetry in structured subgroups. Then robots are designed under the searched symmetry. In this way, SARD can design efficient symmetric robots while covering the original design space, which is theoretically analyzed. We further empirically evaluate SARD on various tasks, and the results show its superior efficiency and generalizability.

cs.AI↗

arXiv2023

Primal-Dual First-Order Methods for Affinely Constrained Multi-Block Saddle Point Problems

We consider the convex-concave saddle point problem $\min_{\mathbf{x}}\max_{\mathbf{y}}Φ(\mathbf{x},\mathbf{y})$, where the decision variables $\mathbf{x}$ and/or $\mathbf{y}$ subject to a multi-block structure and affine coupling constraints, and $Φ(\mathbf{x},\mathbf{y})$ possesses certain separable structure. Although the minimization counterpart of such problem has been widely studied under the topics of ADMM, this minimax problem is rarely investigated. In this paper, a convenient notion of $ε$-saddle point is proposed, under which the convergence rate of several proposed algorithms are analyzed. When only one of $\mathbf{x}$ and $\mathbf{y}$ has multiple blocks and affine constraint, several natural extensions of ADMM are proposed to solve the problem. Depending on the number of blocks and the level of smoothness, $\mathcal{O}(1/T)$ or $\mathcal{O}(1/\sqrt{T})$ convergence rates are derived for our algorithms. When both $\mathbf{x}$ and $\mathbf{y}$ have multiple blocks and affine constraints, a new algorithm called ExtraGradient Method of Multipliers (EGMM) is proposed. Under desirable smoothness condition, an $\mathcal{O}(1/T)$ rate of convergence can be guaranteed regardless of the number of blocks in $\mathbf{x}$ and $\mathbf{y}$. In depth comparison between EGMM (fully primal-dual method) and ADMM (approximate dual method) is made over the multi-block optimization problems to illustrate the advantage of the EGMM.

math.OC↗

arXiv2023

Cost Sharing under Private Valuation and Connection Control

We consider a cost sharing problem on a weighted undirected graph, where all the nodes want to connect to a special node called source, and they need to share the total cost (weights) of the used edges. Each node except for the source has a private valuation of the connection, and it may block others' connections by strategically cutting its adjacent edges to reduce its cost share, which may increase the total cost. We aim to design mechanisms to prevent the nodes from misreporting their valuations and cutting their adjacent edges. We first show that it is impossible for such a mechanism to further satisfy budget balance (cover the total cost) and efficiency (maximize social welfare). Then, we design two feasible cost sharing mechanisms that incentivize each node to offer all its adjacent edges and truthfully report its valuation, and also satisfy either budget balance or efficiency.

cs.GT↗

arXiv2023

On the Sample Complexity and Metastability of Heavy-tailed Policy Search in Continuous Control

Reinforcement learning is a framework for interactive decision-making with incentives sequentially revealed across time without a system dynamics model. Due to its scaling to continuous spaces, we focus on policy search where one iteratively improves a parameterized policy with stochastic policy gradient (PG) updates. In tabular Markov Decision Problems (MDPs), under persistent exploration and suitable parameterization, global optimality may be obtained. By contrast, in continuous space, the non-convexity poses a pathological challenge as evidenced by existing convergence results being mostly limited to stationarity or arbitrary local extrema. To close this gap, we step towards persistent exploration in continuous space through policy parameterizations defined by distributions of heavier tails defined by tail-index parameter alpha, which increases the likelihood of jumping in state space. Doing so invalidates smoothness conditions of the score function common to PG. Thus, we establish how the convergence rate to stationarity depends on the policy's tail index alpha, a Holder continuity parameter, integrability conditions, and an exploration tolerance parameter introduced here for the first time. Further, we characterize the dependence of the set of local maxima on the tail index through an exit and transition time analysis of a suitably defined Markov chain, identifying that policies associated with Levy Processes of a heavier tail converge to wider peaks. This phenomenon yields improved stability to perturbations in supervised learning, which we corroborate also manifests in improved performance of policy search, especially when myopic and farsighted incentives are misaligned.

cs.LG↗

arXiv2022

A Unified Primal-Dual Algorithm Framework for Inequality Constrained Problems

In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers many existing algorithms such as PDHG, Chambolle-Pock (CP), GDA, OGDA and linearized ALM, but also guides us to design a new efficient algorithm called Simi-OGDA (SOGDA). Second, it enables us to study the role of the augmented penalty term in the convergence analysis. Interestingly, a properly selected penalty not only improves the numerical performance of the above methods, but also theoretically enables the convergence of algorithms like PDHG and SOGDA. Under properly designed step sizes and penalty term, our unified framework preserves the $\mathcal{O}(1/N)$ ergodic convergence while not requiring any prior knowledge about the magnitude of the optimal Lagrangian multiplier. Linear convergence rate for affine equality constrained problem is also obtained given appropriate conditions. Finally, numerical experiments on linear programming, $\ell_1$ minimization problem, and multi-block basis pursuit problem demonstrate the efficiency of our methods.

math.OC↗

arXiv2022

A Near-Optimal Primal-Dual Method for Off-Policy Learning in CMDP

As an important framework for safe Reinforcement Learning, the Constrained Markov Decision Process (CMDP) has been extensively studied in the recent literature. However, despite the rich results under various on-policy learning settings, there still lacks some essential understanding of the offline CMDP problems, in terms of both the algorithm design and the information theoretic sample complexity lower bound. In this paper, we focus on solving the CMDP problems where only offline data are available. By adopting the concept of the single-policy concentrability coefficient $C^*$, we establish an $Ω\left(\frac{\min\left\{|\mathcal{S}||\mathcal{A}|,|\mathcal{S}|+I\right\} C^*}{(1-γ)^3ε^2}\right)$ sample complexity lower bound for the offline CMDP problem, where $I$ stands for the number of constraints. By introducing a simple but novel deviation control mechanism, we propose a near-optimal primal-dual learning algorithm called DPDL. This algorithm provably guarantees zero constraint violation and its sample complexity matches the above lower bound except for an $\tilde{\mathcal{O}}((1-γ)^{-1})$ factor. Comprehensive discussion on how to deal with the unknown constant $C^*$ and the potential asynchronous structure on the offline dataset are also included.

cs.LG↗

arXiv2021

Quantumized Microwave Detection Based on $Λ$-Type Three-level Superconducting System: HMM Modeling and Performance Prediction

We adopt artificial $Λ$-type three-level system with superconducting devices for microwave signal detection, where the signal intensity reaches the level of discrete photons instead of continuous waveform. Based on the state transition principles of the three-level system, we propose a statistical model for microwave signal detection. Moreover, we investigate the achievable transmission rate and signal detection based on the statistical model. It is predicted that the proposed detection can achieve significantly higher sensitivity compared with the currently deployed 4G/5G communication system. We further characterize the received signal considering the saturation phonomenon, which reveals negligible performance degradation caused by saturation under weak received power regime.

eess.SP↗

arXiv2021

MARL with General Utilities via Decentralized Shadow Reward Actor-Critic

We posit a new mechanism for cooperation in multi-agent reinforcement learning (MARL) based upon any nonlinear function of the team's long-term state-action occupancy measure, i.e., a \emph{general utility}. This subsumes the cumulative return but also allows one to incorporate risk-sensitivity, exploration, and priors. % We derive the {\bf D}ecentralized {\bf S}hadow Reward {\bf A}ctor-{\bf C}ritic (DSAC) in which agents alternate between policy evaluation (critic), weighted averaging with neighbors (information mixing), and local gradient updates for their policy parameters (actor). DSAC augments the classic critic step by requiring agents to (i) estimate their local occupancy measure in order to (ii) estimate the derivative of the local utility with respect to their occupancy measure, i.e., the "shadow reward". DSAC converges to $ε$-stationarity in $\mathcal{O}(1/ε^{2.5})$ (Theorem \ref{theorem:final}) or faster $\mathcal{O}(1/ε^{2})$ (Corollary \ref{corollary:communication}) steps with high probability, depending on the amount of communications. We further establish the non-existence of spurious stationary points for this problem, that is, DSAC finds the globally optimal policy (Corollary \ref{corollary:global}). Experiments demonstrate the merits of goals beyond the cumulative return in cooperative MARL.

stat.ML↗

arXiv2021

On Lower Iteration Complexity Bounds for the Saddle Point Problems

In this paper, we study the lower iteration complexity bounds for finding the saddle point of a strongly convex and strongly concave saddle point problem: $\min_x\max_yF(x,y)$. We restrict the classes of algorithms in our investigation to be either pure first-order methods or methods using proximal mappings. The existing lower bound result for this type of problems is obtained via the framework of strongly monotone variational inequality problems, which corresponds to the case where the gradient Lipschitz constants ($L_x, L_y$ and $L_{xy}$) and strong convexity/concavity constants ($μ_x$ and $μ_y$) are uniform with respect to variables $x$ and $y$. However, specific to the min-max saddle point problem these parameters are naturally different. Therefore, one is led to finding the best possible lower iteration complexity bounds, specific to the min-max saddle point models. In this paper we present the following results. For the class of pure first-order algorithms, our lower iteration complexity bound is $Ω\left(\sqrt{\frac{L_x}{μ_x}+\frac{L_{xy}^2}{μ_xμ_y}+\frac{L_y}{μ_y}}\cdot\ln\left(\frac{1}ε\right)\right)$, where the term $\frac{L_{xy}^2}{μ_xμ_y}$ explains how the coupling influences the iteration complexity. Under several special parameter regimes, this lower bound has been achieved by corresponding optimal algorithms. However, whether or not the bound under the general parameter regime is optimal remains open. Additionally, for the special case of bilinear coupling problems, given the availability of certain proximal operators, a lower bound of $Ω\left(\sqrt{\frac{L_{xy}^2}{μ_xμ_y}+1}\cdot\ln(\frac{1}ε)\right)$ is established in this paper, and optimal algorithms have already been developed in the literature.

math.OC↗

arXiv2021

On the Convergence and Sample Efficiency of Variance-Reduced Policy Gradient Method

Policy gradient (PG) gives rise to a rich class of reinforcement learning (RL) methods. Recently, there has been an emerging trend to accelerate the existing PG methods such as REINFORCE by the \emph{variance reduction} techniques. However, all existing variance-reduced PG methods heavily rely on an uncheckable importance weight assumption made for every single iteration of the algorithms. In this paper, a simple gradient truncation mechanism is proposed to address this issue. Moreover, we design a Truncated Stochastic Incremental Variance-Reduced Policy Gradient (TSIVR-PG) method, which is able to maximize not only a cumulative sum of rewards but also a general utility function over a policy's long-term visiting distribution. We show an $\tilde{\mathcal{O}}(ε^{-3})$ sample complexity for TSIVR-PG to find an $ε$-stationary policy. By assuming the overparameterizaiton of policy and exploiting the hidden convexity of the problem, we further show that TSIVR-PG converges to global $ε$-optimal policy with $\tilde{\mathcal{O}}(ε^{-2})$ samples.

cs.LG↗

arXiv2021

Stochastic Variance-Reduced Prox-Linear Algorithms for Nonconvex Composite Optimization

We consider minimization of composite functions of the form $f(g(x))+h(x)$, where $f$ and $h$ are convex functions (which can be nonsmooth) and $g$ is a smooth vector mapping. In addition, we assume that $g$ is the average of finite number of component mappings or the expectation over a family of random component mappings. We propose a class of stochastic variance-reduced prox-linear algorithms for solving such problems and bound their sample complexities for finding an $ε$-stationary point in terms of the total number of evaluations of the component mappings and their Jacobians. When $g$ is a finite average of $N$ components, we obtain sample complexity $\mathcal{O}(N+ N^{4/5}ε^{-1})$ for both mapping and Jacobian evaluations. When $g$ is a general expectation, we obtain sample complexities of $\mathcal{O}(ε^{-5/2})$ and $\mathcal{O}(ε^{-3/2})$ for component mappings and their Jacobians respectively. If in addition $f$ is smooth, then improved sample complexities of $\mathcal{O}(N+N^{1/2}ε^{-1})$ and $\mathcal{O}(ε^{-3/2})$ are derived for $g$ being a finite average and a general expectation respectively, for both component mapping and Jacobian evaluations.

math.OC↗

arXiv2021

Multi-Level Composite Stochastic Optimization via Nested Variance Reduction

We consider multi-level composite optimization problems where each mapping in the composition is the expectation over a family of random smooth mappings or the sum of some finite number of smooth mappings. We present a normalized proximal approximate gradient (NPAG) method where the approximate gradients are obtained via nested stochastic variance reduction. In order to find an approximate stationary point where the expected norm of its gradient mapping is less than $ε$, the total sample complexity of our method is $O(ε^{-3})$ in the expectation case, and $O(N+\sqrt{N}ε^{-2})$ in the finite-sum case where $N$ is the total number of functions across all composition levels. In addition, the dependence of our total sample complexity on the number of composition levels is polynomial, rather than exponential as in previous work.

math.OC↗

arXiv2021

Zero-sum risk-sensitive continuous-time stochastic games with unbounded payoff and transition rates and Borel spaces

We study a finite-horizon two-person zero-sum risk-sensitive stochastic game for continuous-time Markov chains and Borel state and action spaces, in which payoff rates, transition rates and terminal reward functions are allowed to be unbounded from below and from above and the policies can be history-dependent. Under suitable conditions, we establish the existence of a solution to the corresponding Shapley equation (SE) by an approximation technique. Then, by the SE and the extension of the Dynkin's formula, we prove the existence of a Nash equilibrium and verify that the value of the stochastic game is the unique solution to the SE. Moreover, we develop a value iteration-type algorithm for approaching to the value of the stochastic game. The convergence of the algorithm is proved by a special contraction operator in our risk-sensitive stochastic game. Finally, we demonstrate our main results by two examples.

math.OC↗