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One of the key challenges in decentralized and federated learning is to design algorithms that efficiently deal with highly heterogeneous data distributions across agents. In this paper, we revisit the analysis of Decentralized Stochastic Gradient Descent algorithm (D-SGD) under data heterogeneity. We exhibit the key role played by a new quantity, called \emph{neighborhood heterogeneity}, on the convergence rate of D-SGD. By coupling the communication topology and the heterogeneity, our analysis sheds light on the poorly understood interplay between these two concepts in decentralized learning. We then argue that neighborhood heterogeneity provides a natural criterion to learn data-dependent topologies that reduce (and can even eliminate) the otherwise detrimental effect of data heterogeneity on the convergence time of D-SGD. For the important case of classification with label skew, we formulate the problem of learning such a good topology as a tractable optimization problem that we solve with a Frank-Wolfe algorithm. As illustrated over a set of simulated and real-world experiments, our approach provides a principled way to design a sparse topology that balances the convergence speed and the per-iteration communication costs of D-SGD under data heterogeneity.

In many computational science and engineering applications, the output of a system of interest corresponding to a given input can be queried at different levels of fidelity with different costs. Typically, low-fidelity data is cheap and abundant, while high-fidelity data is expensive and scarce. In this work we study the reinforcement learning (RL) problem in the presence of multiple environments with different levels of fidelity for a given control task. We focus on improving the RL agent's performance with multifidelity data. Specifically, a multifidelity estimator that exploits the cross-correlations between the low- and high-fidelity returns is proposed to reduce the variance in the estimation of the state-action value function. The proposed estimator, which is based on the method of control variates, is used to design a multifidelity Monte Carlo RL (MFMCRL) algorithm that improves the learning of the agent in the high-fidelity environment. The impacts of variance reduction on policy evaluation and policy improvement are theoretically analyzed by using probability bounds. Our theoretical analysis and numerical experiments demonstrate that for a finite budget of high-fidelity data samples, our proposed MFMCRL agent attains superior performance compared with that of a standard RL agent that uses only the high-fidelity environment data for learning the optimal policy.

Information-directed sampling (IDS) has revealed its potential as a data-efficient algorithm for reinforcement learning (RL). However, theoretical understanding of IDS for Markov Decision Processes (MDPs) is still limited. We develop novel information-theoretic tools to bound the information ratio and cumulative information gain about the learning target. Our theoretical results shed light on the importance of choosing the learning target such that the practitioners can balance the computation and regret bounds. As a consequence, we derive prior-free Bayesian regret bounds for vanilla-IDS which learns the whole environment under tabular finite-horizon MDPs. In addition, we propose a computationally-efficient regularized-IDS that maximizes an additive form rather than the ratio form and show that it enjoys the same regret bound as vanilla-IDS. With the aid of rate-distortion theory, we improve the regret bound by learning a surrogate, less informative environment. Furthermore, we extend our analysis to linear MDPs and prove similar regret bounds for Thompson sampling as a by-product.

Model-based offline optimization with dynamics-aware policy provides a new perspective for policy learning and out-of-distribution generalization, where the learned policy could adapt to different dynamics enumerated at the training stage. But due to the limitation under the offline setting, the learned model could not mimic real dynamics well enough to support reliable out-of-distribution exploration, which still hinders policy to generalize well. To narrow the gap, previous works roughly ensemble randomly initialized models to better approximate the real dynamics. However, such practice is costly and inefficient, and provides no guarantee on how well the real dynamics could be approximated by the learned models, which we name coverability in this paper. We actively address this issue by generating models with provable ability to cover real dynamics in an efficient and controllable way. To that end, we design a distance metric for dynamic models based on the occupancy of policies under the dynamics, and propose an algorithm to generate models optimizing their coverage for the real dynamics. We give a theoretical analysis on the model generation process and proves that our algorithm could provide enhanced coverability. As a downstream task, we train a dynamics-aware policy with minor or no conservative penalty, and experiments demonstrate that our algorithm outperforms prior offline methods on existing offline RL benchmarks. We also discover that policies learned by our method have better zero-shot transfer performance, implying their better generalization.

Many deep reinforcement learning algorithms rely on simple forms of exploration, such as the additive action-noise often used in continuous control domains. Typically, the scaling factor of this action noise is chosen as a hyper-parameter and kept constant during training. In this paper, we analyze how the learned policy is impacted by the noise type, scale, and reducing of the scaling factor over time. We consider the two most prominent types of action-noise: Gaussian and Ornstein-Uhlenbeck noise, and perform a vast experimental campaign by systematically varying the noise type and scale parameter, and by measuring variables of interest like the expected return of the policy and the state space coverage during exploration. For the latter, we propose a novel state-space coverage measure $\operatorname{X}_{\mathcal{U}\text{rel}}$ that is more robust to boundary artifacts than previously proposed measures. Larger noise scales generally increase state space coverage. However, we found that increasing the space coverage using a larger noise scale is often not beneficial. On the contrary, reducing the noise-scale over the training process reduces the variance and generally improves the learning performance. We conclude that the best noise-type and scale are environment dependent, and based on our observations, derive heuristic rules for guiding the choice of the action noise as a starting point for further optimization.

This paper analyzes a two-timescale stochastic algorithm framework for bilevel optimization. Bilevel optimization is a class of problems which exhibit a two-level structure, and its goal is to minimize an outer objective function with variables which are constrained to be the optimal solution to an (inner) optimization problem. We consider the case when the inner problem is unconstrained and strongly convex, while the outer problem is constrained and has a smooth objective function. We propose a two-timescale stochastic approximation (TTSA) algorithm for tackling such a bilevel problem. In the algorithm, a stochastic gradient update with a larger step size is used for the inner problem, while a projected stochastic gradient update with a smaller step size is used for the outer problem. We analyze the convergence rates for the TTSA algorithm under various settings: when the outer problem is strongly convex (resp.~weakly convex), the TTSA algorithm finds an $\mathcal{O}(K^{-2/3})$-optimal (resp.~$\mathcal{O}(K^{-2/5})$-stationary) solution, where $K$ is the total iteration number. As an application, we show that a two-timescale natural actor-critic proximal policy optimization algorithm can be viewed as a special case of our TTSA framework. Importantly, the natural actor-critic algorithm is shown to converge at a rate of $\mathcal{O}(K^{-1/4})$ in terms of the gap in expected discounted reward compared to a global optimal policy.

This paper focuses on improving the resource allocation algorithm in terms of packet delivery ratio (PDR), i.e., the number of successfully received packets sent by end devices (EDs) in a long-range wide-area network (LoRaWAN). Setting the transmission parameters significantly affects the PDR. Employing reinforcement learning (RL), we propose a resource allocation algorithm that enables the EDs to configure their transmission parameters in a distributed manner. We model the resource allocation problem as a multi-armed bandit (MAB) and then address it by proposing a two-phase algorithm named MIX-MAB, which consists of the exponential weights for exploration and exploitation (EXP3) and successive elimination (SE) algorithms. We evaluate the MIX-MAB performance through simulation results and compare it with other existing approaches. Numerical results show that the proposed solution performs better than the existing schemes in terms of convergence time and PDR.

Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of optimisation, one needs to explore high-dimensional spaces representing the problem data or its parameters and thus the computational cost of solving an optimisation problem is connected to the size of the data/variables. This thesis studies the theoretical properties of norm-preserving random embeddings, and their application to several classes of optimisation problems.

The creation and destruction of agents in cooperative multi-agent reinforcement learning (MARL) is a critically under-explored area of research. Current MARL algorithms often assume that the number of agents within a group remains fixed throughout an experiment. However, in many practical problems, an agent may terminate before their teammates. This early termination issue presents a challenge: the terminated agent must learn from the group's success or failure which occurs beyond its own existence. We refer to propagating value from rewards earned by remaining teammates to terminated agents as the Posthumous Credit Assignment problem. Current MARL methods handle this problem by placing these agents in an absorbing state until the entire group of agents reaches a termination condition. Although absorbing states enable existing algorithms and APIs to handle terminated agents without modification, practical training efficiency and resource use problems exist. In this work, we first demonstrate that sample complexity increases with the quantity of absorbing states in a toy supervised learning task for a fully connected network, while attention is more robust to variable size input. Then, we present a novel architecture for an existing state-of-the-art MARL algorithm which uses attention instead of a fully connected layer with absorbing states. Finally, we demonstrate that this novel architecture significantly outperforms the standard architecture on tasks in which agents are created or destroyed within episodes as well as standard multi-agent coordination tasks.

Many tasks in natural language processing can be viewed as multi-label classification problems. However, most of the existing models are trained with the standard cross-entropy loss function and use a fixed prediction policy (e.g., a threshold of 0.5) for all the labels, which completely ignores the complexity and dependencies among different labels. In this paper, we propose a meta-learning method to capture these complex label dependencies. More specifically, our method utilizes a meta-learner to jointly learn the training policies and prediction policies for different labels. The training policies are then used to train the classifier with the cross-entropy loss function, and the prediction policies are further implemented for prediction. Experimental results on fine-grained entity typing and text classification demonstrate that our proposed method can obtain more accurate multi-label classification results.