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1. Model-Based Reinforcement Learning with a Generative Model is Minimax Optimal

   Agarwal, Alekh; Kakade, Sham; Yang, Lin F. (July 2020, Proceedings of Machine Learning Research)

   This work considers the sample and computational complexity of obtaining an $$\epsilon$$-optimal policy in a discounted Markov Decision Process (MDP), given only access to a generative model. In this model, the learner accesses the underlying transition model via a sampling oracle that provides a sample of the next state, when given any state-action pair as input. We are interested in a basic and unresolved question in model based planning: is this naïve “plug-in” approach — where we build the maximum likelihood estimate of the transition model in the MDP from observations and then find an optimal policy in this empirical MDP — non-asymptotically, minimax optimal? Our main result answers this question positively. With regards to computation, our result provides a simpler approach towards minimax optimal planning: in comparison to prior model-free results, we show that using \emph{any} high accuracy, black-box planning oracle in the empirical model suffices to obtain the minimax error rate. The key proof technique uses a leave-one-out analysis, in a novel “absorbing MDP” construction, to decouple the statistical dependency issues that arise in the analysis of model-based planning; this construction may be helpful more generally. 

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2. Teaching a black-box learner

   Dasgupta, S; Hsu, D.J.; Poulis, S. (January 2019, Proceedings of Machine Learning Research)

   null (Ed.)

   One widely-studied model of teaching calls for a teacher to provide the minimal set of labeled examples that uniquely specifies a target concept. The assumption is that the teacher knows the learner’s hypothesis class, which is often not true of real-life teaching scenarios. We consider the problem of teaching a learner whose representation and hypothesis class are unknown—that is, the learner is a black box. We show that a teacher who does not interact with the learner can do no better than providing random examples. We then prove, however, that with interaction, a teacher can efficiently find a set of teaching examples that is a provably good approximation to the optimal set. As an illustration, we show how this scheme can be used to shrink training sets for any family of classifiers: that is, to find an approximately-minimal subset of training instances that yields the same classifier as the entire set. 

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3. Structured Reinforcement Learning for Incentivized Stochastic Covert Optimization

   https://doi.org/10.1109/LCSYS.2024.3406543  

   Jain, Adit; Krishnamurthy, Vikram (January 2024, IEEE Control Systems Letters)

   This letter studies how a stochastic gradient algorithm (SG) can be controlled to hide the estimate of the local stationary point from an eavesdropper. Such prob- lems are of significant interest in distributed optimization settings like federated learning and inventory management. A learner queries a stochastic oracle and incentivizes the oracle to obtain noisy gradient measurements and per- form SG. The oracle probabilistically returns either a noisy gradient of the function or a non-informative measure- ment, depending on the oracle state and incentive. The learner’s query and incentive are visible to an eavesdropper who wishes to estimate the stationary point. This letter formulates the problem of the learner performing covert optimization by dynamically incentivizing the stochastic oracle and obfuscating the eavesdropper as a finite-horizon Markov decision process (MDP). Using conditions for interval-dominance on the cost and transition probability structure, we show that the optimal policy for the MDP has a monotone threshold structure. We propose searching for the optimal stationary policy with the threshold structure using a stochastic approximation algorithm and a multi– armed bandit approach. The effectiveness of our methods is numerically demonstrated on a covert federated learning hate-speech classification task. 

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4. Planning with State Abstractions for Non-Markovian Task Specifications

   Yoonseon Oh, Roma Patel (January 2019, Robotics science and systems)

   Abstract—Often times, we specify tasks for a robot using tem- poral language that can also span different levels of abstraction. The example command “go to the kitchen before going to the second floor” contains spatial abstraction, given that “floor” consists of individual rooms that can also be referred to in isolation (“kitchen”, for example). There is also a temporal ordering of events, defined by the word “before”. Previous works have used Linear Temporal Logic (LTL) to interpret temporal language (such as “before”), and Abstract Markov Decision Processes (AMDPs) to interpret hierarchical abstractions (such as “kitchen” and “second floor”), separately. To handle both types of commands at once, we introduce the Abstract Product Markov Decision Process (AP-MDP), a novel approach capable of representing non-Markovian reward functions at different levels of abstractions. The AP-MDP framework translates LTL into its corresponding automata, creates a product Markov Decision Process (MDP) of the LTL specification and the environment MDP, and decomposes the problem into subproblems to enable efficient planning with abstractions. AP-MDP performs faster than a non-hierarchical method of solving LTL problems in over 95% of tasks, and this number only increases as the size of the en- vironment domain increases. We also present a neural sequence- to-sequence model trained to translate language commands into LTL expression, and a new corpus of non-Markovian language commands spanning different levels of abstraction. We test our framework with the collected language commands on a drone, demonstrating that our approach enables a robot to efficiently solve temporal commands at different levels of abstraction. 

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5. Teaching an Active Learner with Contrastive Examples

   Wang, Chaoqi; Singla, Adish; Chen, Yuxin (December 2021, Advances in neural information processing systems)

   We study the problem of active learning with the added twist that the learner is assisted by a helpful teacher. We consider the following natural interaction protocol: At each round, the learner proposes a query asking for the label of an instance xq, the teacher provides the requested label {xq,yq} along with explanatory information to guide the learning process. In this paper, we view this information in the form of an additional contrastive example ({xc,yc}) where xc is picked from a set constrained by xq (e.g., dissimilar instances with the same label). Our focus is to design a teaching algorithm that can provide an informative sequence of contrastive examples to the learner to speed up the learning process. We show that this leads to a challenging sequence optimization problem where the algorithm's choices at a given round depend on the history of interactions. We investigate an efficient teaching algorithm that adaptively picks these contrastive examples. We derive strong performance guarantees for our algorithm based on two problem-dependent parameters and further show that for specific types of active learners (e.g., a generalized binary search learner), the proposed teaching algorithm exhibits strong approximation guarantees. Finally, we illustrate our bounds and demonstrate the effectiveness of our teaching framework via two numerical case studies. 

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