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1. Controlling Federated Learning for Covertness

   Jain, Adit; Krishnamurthy, Vikram (February 2024, Transactions on machine learning research)

   A learner aims to minimize a function f by repeatedly querying a distributed oracle that provides noisy gradient evaluations. At the same time, the learner seeks to hide arg min f from a malicious eavesdropper that observes the learner’s queries. This paper considers the problem of covert or learner-private optimization, where the learner has to dynamically choose between learning and obfuscation by exploiting the stochasticity. The problem of controlling the stochastic gradient algorithm for covert optimization is modeled as a Markov decision process, and we show that the dynamic programming operator has a supermodular structure implying that the optimal policy has a monotone threshold structure. A computationally efficient policy gradient algorithm is proposed to search for the optimal querying policy without knowledge of the transition probabilities. As a practical application, our methods are demonstrated on a hate speech classification task in a federated setting where an eavesdropper can use the optimal weights to generate toxic content, which is more easily misclassified. Numerical results show that when the learner uses the optimal policy, an eavesdropper can only achieve a validation accuracy of 52% with no information and 69% when it has a public dataset with 10% positive samples compared to 83% when the learner employs a greedy policy. 

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2. Adaptive Incentive Design for Markov Decision Processes with Unknown Rewards

   Ma, Haoxiang; Han, Shuo; Hemida, Ahmed; Kamhoua, Charles A; Fu, Jie (March 2025, Transactions on Machine Learning Research)

   Poupart, Pascal (Ed.)

   Incentive design, also known as model design or environment design for Markov decision processes(MDPs), refers to a class of problems in which a leader can incentivize his follower by modifying the follower's reward function, in anticipation that the follower's optimal policy in the resulting MDP can be desirable for the leader's objective. In this work, we propose gradient-ascent algorithms to compute the leader's optimal incentive design, despite the lack of knowledge about the follower's reward function. First, we formulate the incentive design problem as a bi-level optimization problem and demonstrate that, by the softmax temporal consistency between the follower's policy and value function, the bi-level optimization problem can be reduced to single-level optimization, for which a gradient-based algorithm can be developed to optimize the leader's objective. We establish several key properties of incentive design in MDPs and prove the convergence of the proposed gradient-based method. Next, we show that the gradient terms can be estimated from observations of the follower's best response policy, enabling the use of a stochastic gradient-ascent algorithm to compute a locally optimal incentive design without knowing or learning the follower's reward function. Finally, we analyze the conditions under which an incentive design remains optimal for two different rewards which are policy invariant. The effectiveness of the proposed algorithm is demonstrated using a small probabilistic transition system and a stochastic gridworld. 

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3. Finite-Sample Bounds for Adaptive Inverse Reinforcement Learning Using Passive Langevin Dynamics

   https://doi.org/10.1109/TIT.2025.3555479  

   Snow, Luke; Krishnamurthy, Vikram (June 2025, IEEE Transactions on Information Theory)

   This paper provides a finite-sample analysis of a passive stochastic gradient Langevin dynamics (PSGLD) algo- rithm. This algorithm is designed to achieve adaptive inverse reinforcement learning (IRL). Adaptive IRL aims to estimate the cost function of a forward learner performing a stochastic gradient algorithm (e.g., policy gradient reinforcement learning) by observing their estimates in real-time. The PSGLD algorithm is considered passive because it incorporates noisy gradients provided by an external stochastic gradient algorithm (forward learner), of which it has no control. The PSGLD algorithm acts as a randomized sampler to achieve adaptive IRL by reconstructing the forward learner’s cost function nonparametrically from the stationary measure of a Langevin diffusion. This paper analyzes the non-asymptotic (finite-sample) performance; we provide explicit bounds on the 2-Wasserstein distance between PSGLD algorithm sample measure and the stationary measure encoding the cost function, and provide guarantees for a kernel density estimation scheme which reconstructs the cost function from empirical samples. Our analysis uses tools from the study of Markov diffusion operators. The derived bounds have both practical and theoretical significance. They provide finite-time guarantees for an adaptive IRL mechanism, and substantially generalize the analytical framework of a line of research in passive stochastic gradient algorithms. 

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4. Adaptive Online Estimation of Piecewise Polynomial Trends

   Baby, Dheeraj; Wang, Yu-Xiang (December 2020, NeurIPS 2020)

   null (Ed.)

   We consider the framework of non-stationary stochastic optimization (Besbes et al., 2015) with squared error losses and noisy gradient feedback where the dynamic regret of an online learner against a time varying comparator sequence is studied. Motivated from the theory of non-parametric regression, we introduce a new variational constraint that enforces the comparator sequence to belong to a discrete k^{th} order Total Variation ball of radius C_n. This variational constraint models comparators that have piece-wise polynomial structure which has many relevant practical applications (Tibshirani, 2014). By establishing connections to the theory of wavelet based non-parametric regression, we design a polynomial time algorithm that achieves the nearly optimal dynamic regret of ~O(n^{1/(2k+3)} C_n^{2/(2k+3)}). The proposed policy is adaptive to the unknown radius C_n. Further, we show that the same policy is minimax optimal for several other non-parametric families of interest. 

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5. The Complexity of Making the Gradient Small in Stochastic Convex Optimization

   Foster, Dylan Y; Sekhari, Ayush; Shamir, Ohad; Srebro, Nathan; Sridharan, Karthik; Woodworth, Blake (June 2019, Proceedings of Machine Learning Research)

   We give nearly matching upper and lower bounds on the oracle complexity of finding ϵ-stationary points (∥∇F(x)∥≤ϵ in stochastic convex optimization. We jointly analyze the oracle complexity in both the local stochastic oracle model and the global oracle (or, statistical learning) model. This allows us to decompose the complexity of finding near-stationary points into optimization complexity and sample complexity, and reveals some surprising differences between the complexity of stochastic optimization versus learning. Notably, we show that in the global oracle/statistical learning model, only logarithmic dependence on smoothness is required to find a near-stationary point, whereas polynomial dependence on smoothness is necessary in the local stochastic oracle model. In other words, the separation in complexity between the two models can be exponential, and the folklore understanding that smoothness is required to find stationary points is only weakly true for statistical learning. Our upper bounds are based on extensions of a recent “recursive regularization” technique proposed by Allen-Zhu (2018). We show how to extend the technique to achieve near-optimal rates, and in particular show how to leverage the extra information available in the global oracle model. Our algorithm for the global model can be implemented efficiently through finite sum methods, and suggests an interesting new computational-statistical tradeoff 

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