Principled Penalty-based Methods for Bilevel Reinforcement Learning and RLHF

Bilevel optimization has been recently applied to many machine learning tasks. However, their applications have been restricted to the supervised learning setting, where static objective functions with benign structures are considered. But bilevel problems such as incentive design, inverse reinforcement learning (RL), and RL from human feedback (RLHF) are often modeled as dynamic objective functions that go beyond the simple static objective structures, which pose significant challenges of using existing bilevel solutions. To tackle this new class of bilevel problems, we introduce the first principled algorithmic framework for solving bilevel RL problems through the lens of penalty formulation. We provide theoretical studies of the problem landscape and its penalty-based (policy) gradient algorithms. We demonstrate the effectiveness of our algorithms via simulations in the Stackelberg Markov game, RL from human feedback and incentive design.

Joint Unsupervised and Supervised Training for Automatic Speech Recognition via Bilevel Optimization

In this paper, we present a novel bilevel optimization-based training approach to training acoustic models for automatic speech recognition (ASR) tasks that we term {bi-level joint unsupervised and supervised training (BL-JUST)}. {BL-JUST employs a lower and upper level optimization with an unsupervised loss and a supervised loss respectively, leveraging recent advances in penalty-based bilevel optimization to solve this challenging ASR problem with affordable complexity and rigorous convergence guarantees.} To evaluate BL-JUST, extensive experiments on the LibriSpeech and TED-LIUM v2 datasets have been conducted. BL-JUST achieves superior performance over the commonly used pre-training followed by fine-tuning strategy.

On Penalty-based Bilevel Gradient Descent Method

Bilevel optimization enjoys a wide range of applications in hyper-parameter optimization, meta-learning and reinforcement learning. However, bilevel optimization problems are difficult to solve. Recent progress on scalable bilevel algorithms mainly focuses on bilevel optimization problems where the lower-level objective is either strongly convex or unconstrained. In this work, we tackle the bilevel problem through the lens of the penalty method. We show that under certain conditions, the penalty reformulation recovers the solutions of the original bilevel problem. Further, we propose the penalty-based bilevel gradient descent (PBGD) algorithm and establish its finite-time convergence for the constrained bilevel problem without lower-level strong convexity. Experiments showcase the efficiency of the proposed PBGD algorithm.

Alternating Implicit Projected SGD and Its Efficient Variants for Equality-constrained Bilevel Optimization

Stochastic bilevel optimization, which captures the inherent nested structure of machine learning problems, is gaining popularity in many recent applications. Existing works on bilevel optimization mostly consider either unconstrained problems or constrained upper-level problems. This paper considers the stochastic bilevel optimization problems with equality constraints both in the upper and lower levels. By leveraging the special structure of the equality constraints problem, the paper first presents an alternating implicit projected SGD approach and establishes the $\tilde{\cal O}(\epsilon^{-2})$ sample complexity that matches the state-of-the-art complexity of ALSET \citep{chen2021closing} for unconstrained bilevel problems. To further save the cost of projection, the paper presents two alternating implicit projection-efficient SGD approaches, where one algorithm enjoys the $\tilde{\cal O}(\epsilon^{-2}/T)$ upper-level and ${\cal O}(\epsilon^{-1.5}/T^{\frac{3}{4}})$ lower-level projection complexity with ${\cal O}(T)$ lower-level batch size, and the other one enjoys $\tilde{\cal O}(\epsilon^{-1.5})$ upper-level and lower-level projection complexity with ${\cal O}(1)$ batch size. Application to federated bilevel optimization has been presented to showcase the empirical performance of our algorithms. Our results demonstrate that equality-constrained bilevel optimization with strongly-convex lower-level problems can be solved as efficiently as stochastic single-level optimization problems.

Mitigating Gradient Bias in Multi-objective Learning: A Provably Convergent Stochastic Approach

Machine learning problems with multiple objective functions appear either in learning with multiple criteria where learning has to make a trade-off between multiple performance metrics such as fairness, safety and accuracy; or, in multi-task learning where multiple tasks are optimized jointly, sharing inductive bias between them. This problems are often tackled by the multi-objective optimization framework. However, existing stochastic multi-objective gradient methods and its variants (e.g., MGDA, PCGrad, CAGrad, etc.) all adopt a biased noisy gradient direction, which leads to degraded empirical performance. To this end, we develop a stochastic Multi-objective gradient Correction (MoCo) method for multi-objective optimization. The unique feature of our method is that it can guarantee convergence without increasing the batch size even in the non-convex setting. Simulations on multi-task supervised and reinforcement learning demonstrate the effectiveness of our method relative to state-of-the-art methods.

A Single-Timescale Analysis For Stochastic Approximation With Multiple Coupled Sequences

Stochastic approximation (SA) with multiple coupled sequences has found broad applications in machine learning such as bilevel learning and reinforcement learning (RL). In this paper, we study the finite-time convergence of nonlinear SA with multiple coupled sequences. Different from existing multi-timescale analysis, we seek for scenarios where a fine-grained analysis can provide the tight performance guarantee for multi-sequence single-timescale SA (STSA). At the heart of our analysis is the smoothness property of the fixed points in multi-sequence SA that holds in many applications. When all sequences have strongly monotone increments, we establish the iteration complexity of $\mathcal{O}(\epsilon^{-1})$ to achieve $\epsilon$-accuracy, which improves the existing $\mathcal{O}(\epsilon^{-1.5})$ complexity for two coupled sequences. When all but the main sequence have strongly monotone increments, we establish the iteration complexity of $\mathcal{O}(\epsilon^{-2})$. The merit of our results lies in that applying them to stochastic bilevel and compositional optimization problems, as well as RL problems leads to either relaxed assumptions or improvements over their existing performance guarantees.

Asynchronous Advantage Actor Critic: Non-asymptotic Analysis and Linear Speedup

Asynchronous and parallel implementation of standard reinforcement learning (RL) algorithms is a key enabler of the tremendous success of modern RL. Among many asynchronous RL algorithms, arguably the most popular and effective one is the asynchronous advantage actor-critic (A3C) algorithm. Although A3C is becoming the workhorse of RL, its theoretical properties are still not well-understood, including the non-asymptotic analysis and the performance gain of parallelism (a.k.a. speedup). This paper revisits the A3C algorithm with TD(0) for the critic update, termed A3C-TD(0), with provable convergence guarantees. With linear value function approximation for the TD update, the convergence of A3C-TD(0) is established under both i.i.d. and Markovian sampling. Under i.i.d. sampling, A3C-TD(0) obtains sample complexity of $\mathcal{O}(\epsilon^{-2.5}/N)$ per worker to achieve $\epsilon$ accuracy, where $N$ is the number of workers. Compared to the best-known sample complexity of $\mathcal{O}(\epsilon^{-2.5})$ for two-timescale AC, A3C-TD(0) achieves \emph{linear speedup}, which justifies the advantage of parallelism and asynchrony in AC algorithms theoretically for the first time. Numerical tests on synthetically generated instances and OpenAI Gym environments have been provided to verify our theoretical analysis.

Multi-object Tracking via End-to-end Tracklet Searching and Ranking

Recent works in multiple object tracking use sequence model to calculate the similarity score between the detections and the previous tracklets. However, the forced exposure to ground-truth in the training stage leads to the training-inference discrepancy problem, i.e., exposure bias, where association error could accumulate in the inference and make the trajectories drift. In this paper, we propose a novel method for optimizing tracklet consistency, which directly takes the prediction errors into account by introducing an online, end-to-end tracklet search training process. Notably, our methods directly optimize the whole tracklet score instead of pairwise affinity. With sequence model as appearance encoders of tracklet, our tracker achieves remarkable performance gain from conventional tracklet association baseline. Our methods have also achieved state-of-the-art in MOT15~17 challenge benchmarks using public detection and online settings.

Adaptive Temporal Difference Learning with Linear Function Approximation

This paper revisits the celebrated temporal difference (TD) learning algorithm for the policy evaluation in reinforcement learning. Typically, the performance of the plain-vanilla TD algorithm is sensitive to the choice of stepsizes. Oftentimes, TD suffers from slow convergence. Motivated by the tight connection between the TD learning algorithm and the stochastic gradient methods, we develop the first adaptive variant of the TD learning algorithm with linear function approximation that we term AdaTD. In contrast to the original TD, AdaTD is robust or less sensitive to the choice of stepsizes. Analytically, we establish that to reach an $\epsilon$ accuracy, the number of iterations needed is $\tilde{O}(\epsilon^2\ln^4\frac{1}{\epsilon}/\ln^4\frac{1}{\rho})$, where $\rho$ represents the speed of the underlying Markov chain converges to the stationary distribution. This implies that the iteration complexity of AdaTD is no worse than that of TD in the worst case. Going beyond TD, we further develop an adaptive variant of TD($\lambda$), which is referred to as AdaTD($\lambda$). We evaluate the empirical performance of AdaTD and AdaTD($\lambda$) on several standard reinforcement learning tasks in OpenAI Gym on both linear and nonlinear function approximation, which demonstrate the effectiveness of our new approaches over existing ones.

Real Time Visual Tracking using Spatial-Aware Temporal Aggregation Network

More powerful feature representations derived from deep neural networks benefit visual tracking algorithms widely. However, the lack of exploitation on temporal information prevents tracking algorithms from adapting to appearances changing or resisting to drift. This paper proposes a correlation filter based tracking method which aggregates historical features in a spatial-aligned and scale-aware paradigm. The features of historical frames are sampled and aggregated to search frame according to a pixel-level alignment module based on deformable convolutions. In addition, we also use a feature pyramid structure to handle motion estimation at different scales, and address the different demands on feature granularity between tracking losses and deformation offset learning. By this design, the tracker, named as Spatial-Aware Temporal Aggregation network (SATA), is able to assemble appearances and motion contexts of various scales in a time period, resulting in better performance compared to a single static image. Our tracker achieves leading performance in OTB2013, OTB2015, VOT2015, VOT2016 and LaSOT, and operates at a real-time speed of 26 FPS, which indicates our method is effective and practical. Our code will be made publicly available at \href{https://github.com/ecart18/SATA}{https://github.com/ecart18/SATA}.