Geometric Foundations of Tuning without Forgetting in Neural ODEs

In our earlier work, we introduced the principle of Tuning without Forgetting (TwF) for sequential training of neural ODEs, where training samples are added iteratively and parameters are updated within the subspace of control functions that preserves the end-point mapping at previously learned samples on the manifold of output labels in the first-order approximation sense. In this letter, we prove that this parameter subspace forms a Banach submanifold of finite codimension under nonsingular controls, and we characterize its tangent space. This reveals that TwF corresponds to a continuation/deformation of the control function along the tangent space of this Banach submanifold, providing a theoretical foundation for its mapping-preserving (not forgetting) during the sequential training exactly, beyond first-order approximation.

A Soft Inducement Framework for Incentive-Aided Steering of No-Regret Players

In this work, we investigate a steering problem in a mediator-augmented two-player normal-form game, where the mediator aims to guide players toward a specific action profile through information and incentive design. We first characterize the games for which successful steering is possible. Moreover, we establish that steering players to any desired action profile is not always achievable with information design alone, nor when accompanied with sublinear payment schemes. Consequently, we derive a lower bound on the constant payments required per round to achieve this goal. To address these limitations incurred with information design, we introduce an augmented approach that involves a one-shot information design phase before the start of the repeated game, transforming the prior interaction into a Stackelberg game. Finally, we theoretically demonstrate that this approach improves the convergence rate of players' action profiles to the target point by a constant factor with high probability, and support it with empirical results.

Aggregate Fictitious Play for Learning in Anonymous Polymatrix Games (Extended Version)

Fictitious play (FP) is a well-studied algorithm that enables agents to learn Nash equilibrium in games with certain reward structures. However, when agents have no prior knowledge of the reward functions, FP faces a major challenge: the joint action space grows exponentially with the number of agents, which slows down reward exploration. Anonymous games offer a structure that mitigates this issue. In these games, the rewards depend only on the actions taken; not on who is taking which action. Under such a structure, we introduce aggregate fictitious play (agg-FP), a variant of FP where each agent tracks the frequency of the number of other agents playing each action, rather than these agents' individual actions. We show that in anonymous polymatrix games, agg-FP converges to a Nash equilibrium under the same conditions as classical FP. In essence, by aggregating the agents' actions, we reduce the action space without losing the convergence guarantees. Using simulations, we provide empirical evidence on how this reduction accelerates convergence.

InterQ: A DQN Framework for Optimal Intermittent Control

In this letter, we explore the communication-control co-design of discrete-time stochastic linear systems through reinforcement learning. Specifically, we examine a closed-loop system involving two sequential decision-makers: a scheduler and a controller. The scheduler continuously monitors the system's state but transmits it to the controller intermittently to balance the communication cost and control performance. The controller, in turn, determines the control input based on the intermittently received information. Given the partially nested information structure, we show that the optimal control policy follows a certainty-equivalence form. Subsequently, we analyze the qualitative behavior of the scheduling policy. To develop the optimal scheduling policy, we propose InterQ, a deep reinforcement learning algorithm which uses a deep neural network to approximate the Q-function. Through extensive numerical evaluations, we analyze the scheduling landscape and further compare our approach against two baseline strategies: (a) a multi-period periodic scheduling policy, and (b) an event-triggered policy. The results demonstrate that our proposed method outperforms both baselines. The open source implementation can be found at https://github.com/AC-sh/InterQ.

Remote Estimation Games with Random Walk Processes: Stackelberg Equilibrium

Remote estimation is a crucial element of real time monitoring of a stochastic process. While most of the existing works have concentrated on obtaining optimal sampling strategies, motivated by malicious attacks on cyber-physical systems, we model sensing under surveillance as a game between an attacker and a defender. This introduces strategic elements to conventional remote estimation problems. Additionally, inspired by increasing detection capabilities, we model an element of information leakage for each player. Parameterizing the game in terms of uncertainty on each side, information leakage, and cost of sampling, we consider the Stackelberg Equilibrium (SE) concept where one of the players acts as the leader and the other one as the follower. By focusing our attention on stationary probabilistic sampling policies, we characterize the SE of this game and provide simulations to show the efficacy of our results.

Structure Matters: Dynamic Policy Gradient

In this work, we study $\gamma$-discounted infinite-horizon tabular Markov decision processes (MDPs) and introduce a framework called dynamic policy gradient (DynPG). The framework directly integrates dynamic programming with (any) policy gradient method, explicitly leveraging the Markovian property of the environment. DynPG dynamically adjusts the problem horizon during training, decomposing the original infinite-horizon MDP into a sequence of contextual bandit problems. By iteratively solving these contextual bandits, DynPG converges to the stationary optimal policy of the infinite-horizon MDP. To demonstrate the power of DynPG, we establish its non-asymptotic global convergence rate under the tabular softmax parametrization, focusing on the dependencies on salient but essential parameters of the MDP. By combining classical arguments from dynamic programming with more recent convergence arguments of policy gradient schemes, we prove that softmax DynPG scales polynomially in the effective horizon $(1-\gamma)^{-1}$. Our findings contrast recent exponential lower bound examples for vanilla policy gradient.

Optimizing Profitability in Timely Gossip Networks

We consider a communication system where a group of users, interconnected in a bidirectional gossip network, wishes to follow a time-varying source, e.g., updates on an event, in real-time. The users wish to maintain their expected version ages below a threshold, and can either rely on gossip from their neighbors or directly subscribe to a server publishing about the event, if the former option does not meet the timeliness requirements. The server wishes to maximize its profit by increasing subscriptions from users and minimizing event sampling frequency to reduce costs. This leads to a Stackelberg game between the server and the users where the sender is the leader deciding its sampling frequency and the users are the followers deciding their subscription strategies. We investigate equilibrium strategies for low-connectivity and high-connectivity topologies.

How to Make Money From Fresh Data: Subscription Strategies in Age-Based Systems

We consider a communication system consisting of a server that tracks and publishes updates about a time-varying data source or event, and a gossip network of users interested in closely tracking the event. The timeliness of the information is measured through the version age of information. The users wish to have their expected version ages remain below a threshold, and have the option to either rely on gossip from their neighbors or subscribe to the server directly to follow updates about the event if the former option does not meet the timeliness requirements. The server wishes to maximize its profit by increasing the number of subscribers and reducing costs associated with the frequent sampling of the event. We model the problem setup as a Stackelberg game between the server and the users, where the server commits to a frequency of sampling the event, and the users make decisions on whether to subscribe or not. As an initial work, we focus on directed networks with unidirectional flow of information and obtain the optimal equilibrium strategies for all the players. We provide simulation results to confirm the theoretical findings and provide additional insights.

Control Theoretic Approach to Fine-Tuning and Transfer Learning

Given a training set in the form of a paired $(\mathcal{X},\mathcal{Y})$, we say that the control system $\dot{x} = f(x,u)$ has learned the paired set via the control $u^*$ if the system steers each point of $\mathcal{X}$ to its corresponding target in $\mathcal{Y}$. Most existing methods for finding a control function $u^*$ require learning of a new control function if the training set is updated. To overcome this limitation, we introduce the concept of $\textit{tuning without forgetting}$. We develop $\textit{an iterative algorithm}$ to tune the control function $u^*$ when the training set expands, whereby points already in the paired set are still matched, and new training samples are learned. More specifically, at each update of our method, the control $u^*$ is projected onto the kernel of the end-point mapping generated by the controlled dynamics at the learned samples. It ensures keeping the end points for the previously learned samples constant while iteratively learning additional samples. Our work contributes to the scalability of control methods, offering a novel approach to adaptively handle training set expansions.

Efficient Interactive LLM Serving with Proxy Model-based Sequence Length Prediction

Large language models (LLMs) have been driving a new wave of interactive AI applications across numerous domains. However, efficiently serving LLM inference requests is challenging due to their unpredictable execution times originating from the autoregressive nature of generative models. Existing LLM serving systems exploit first-come-first-serve (FCFS) scheduling, suffering from head-of-line blocking issues. To address the non-deterministic nature of LLMs and enable efficient interactive LLM serving, we present a speculative shortest-job-first (SSJF) scheduler that uses a light proxy model to predict LLM output sequence lengths. Our open-source SSJF implementation does not require changes to memory management or batching strategies. Evaluations on real-world datasets and production workload traces show that SSJF reduces average job completion times by 30.5-39.6% and increases throughput by 2.2-3.6x compared to FCFS schedulers, across no batching, dynamic batching, and continuous batching settings.