Preserving Plasticity in Continual Learning with Adaptive Linearity Injection

Loss of plasticity in deep neural networks is the gradual reduction in a model's capacity to incrementally learn and has been identified as a key obstacle to learning in non-stationary problem settings. Recent work has shown that deep linear networks tend to be resilient towards loss of plasticity. Motivated by this observation, we propose Adaptive Linearization (AdaLin), a general approach that dynamically adapts each neuron's activation function to mitigate plasticity loss. Unlike prior methods that rely on regularization or periodic resets, AdaLin equips every neuron with a learnable parameter and a gating mechanism that injects linearity into the activation function based on its gradient flow. This adaptive modulation ensures sufficient gradient signal and sustains continual learning without introducing additional hyperparameters or requiring explicit task boundaries. When used with conventional activation functions like ReLU, Tanh, and GeLU, we demonstrate that AdaLin can significantly improve performance on standard benchmarks, including Random Label and Permuted MNIST, Random Label and Shuffled CIFAR-10, and Class-Split CIFAR-100. Furthermore, its efficacy is shown in more complex scenarios, such as class-incremental learning on CIFAR-100 with a ResNet-18 backbone, and in mitigating plasticity loss in off-policy reinforcement learning agents. We perform a systematic set of ablations that show that neuron-level adaptation is crucial for good performance and analyze a number of metrics in the network that might be correlated to loss of plasticity.

Rethinking the Global Convergence of Softmax Policy Gradient with Linear Function Approximation

Policy gradient (PG) methods have played an essential role in the empirical successes of reinforcement learning. In order to handle large state-action spaces, PG methods are typically used with function approximation. In this setting, the approximation error in modeling problem-dependent quantities is a key notion for characterizing the global convergence of PG methods. We focus on Softmax PG with linear function approximation (referred to as $\texttt{Lin-SPG}$) and demonstrate that the approximation error is irrelevant to the algorithm's global convergence even for the stochastic bandit setting. Consequently, we first identify the necessary and sufficient conditions on the feature representation that can guarantee the asymptotic global convergence of $\texttt{Lin-SPG}$. Under these feature conditions, we prove that $T$ iterations of $\texttt{Lin-SPG}$ with a problem-specific learning rate result in an $O(1/T)$ convergence to the optimal policy. Furthermore, we prove that $\texttt{Lin-SPG}$ with any arbitrary constant learning rate can ensure asymptotic global convergence to the optimal policy.

Small steps no more: Global convergence of stochastic gradient bandits for arbitrary learning rates

We provide a new understanding of the stochastic gradient bandit algorithm by showing that it converges to a globally optimal policy almost surely using \emph{any} constant learning rate. This result demonstrates that the stochastic gradient algorithm continues to balance exploration and exploitation appropriately even in scenarios where standard smoothness and noise control assumptions break down. The proofs are based on novel findings about action sampling rates and the relationship between cumulative progress and noise, and extend the current understanding of how simple stochastic gradient methods behave in bandit settings.

Improving OOD Generalization of Pre-trained Encoders via Aligned Embedding-Space Ensembles

The quality of self-supervised pre-trained embeddings on out-of-distribution (OOD) data is poor without fine-tuning. A straightforward and simple approach to improving the generalization of pre-trained representation to OOD data is the use of deep ensembles. However, obtaining an effective ensemble in the embedding space with only unlabeled data remains an unsolved problem. We first perform a theoretical analysis that reveals the relationship between individual hyperspherical embedding spaces in an ensemble. We then design a principled method to align these embedding spaces in an unsupervised manner. Experimental results on the MNIST dataset show that our embedding-space ensemble method improves pre-trained embedding quality on in-distribution and OOD data compared to single encoders.

Fast Convergence of Softmax Policy Mirror Ascent

Natural policy gradient (NPG) is a common policy optimization algorithm and can be viewed as mirror ascent in the space of probabilities. Recently, Vaswani et al. [2021] introduced a policy gradient method that corresponds to mirror ascent in the dual space of logits. We refine this algorithm, removing its need for a normalization across actions and analyze the resulting method (referred to as SPMA). For tabular MDPs, we prove that SPMA with a constant step-size matches the linear convergence of NPG and achieves a faster convergence than constant step-size (accelerated) softmax policy gradient. To handle large state-action spaces, we extend SPMA to use a log-linear policy parameterization. Unlike that for NPG, generalizing SPMA to the linear function approximation (FA) setting does not require compatible function approximation. Unlike MDPO, a practical generalization of NPG, SPMA with linear FA only requires solving convex softmax classification problems. We prove that SPMA achieves linear convergence to the neighbourhood of the optimal value function. We extend SPMA to handle non-linear FA and evaluate its empirical performance on the MuJoCo and Atari benchmarks. Our results demonstrate that SPMA consistently achieves similar or better performance compared to MDPO, PPO and TRPO.

Towards Principled, Practical Policy Gradient for Bandits and Tabular MDPs

We consider (stochastic) softmax policy gradient (PG) methods for bandits and tabular Markov decision processes (MDPs). While the PG objective is non-concave, recent research has used the objective's smoothness and gradient domination properties to achieve convergence to an optimal policy. However, these theoretical results require setting the algorithm parameters according to unknown problem-dependent quantities (e.g. the optimal action or the true reward vector in a bandit problem). To address this issue, we borrow ideas from the optimization literature to design practical, principled PG methods in both the exact and stochastic settings. In the exact setting, we employ an Armijo line-search to set the step-size for softmax PG and empirically demonstrate a linear convergence rate. In the stochastic setting, we utilize exponentially decreasing step-sizes, and characterize the convergence rate of the resulting algorithm. We show that the proposed algorithm offers similar theoretical guarantees as the state-of-the art results, but does not require the knowledge of oracle-like quantities. For the multi-armed bandit setting, our techniques result in a theoretically-principled PG algorithm that does not require explicit exploration, the knowledge of the reward gap, the reward distributions, or the noise. Finally, we empirically compare the proposed methods to PG approaches that require oracle knowledge, and demonstrate competitive performance.

From Inverse Optimization to Feasibility to ERM

Inverse optimization involves inferring unknown parameters of an optimization problem from known solutions, and is widely used in fields such as transportation, power systems and healthcare. We study the contextual inverse optimization setting that utilizes additional contextual information to better predict the unknown problem parameters. We focus on contextual inverse linear programming (CILP), addressing the challenges posed by the non-differentiable nature of LPs. For a linear prediction model, we reduce CILP to a convex feasibility problem allowing the use of standard algorithms such as alternating projections. The resulting algorithm for CILP is equipped with a linear convergence guarantee without additional assumptions such as degeneracy or interpolation. Next, we reduce CILP to empirical risk minimization (ERM) on a smooth, convex loss that satisfies the Polyak-Lojasiewicz condition. This reduction enables the use of scalable first-order optimization methods to solve large non-convex problems, while maintaining theoretical guarantees in the convex setting. Finally, we experimentally validate our approach on both synthetic and real-world problems, and demonstrate improved performance compared to existing methods.

Noise-adaptive (Accelerated) Stochastic Heavy-Ball Momentum

We analyze the convergence of stochastic heavy ball (SHB) momentum in the smooth, strongly-convex setting. Kidambi et al. (2018) show that SHB (with small mini-batches) cannot attain an accelerated rate of convergence even for quadratics, and conjecture that the practical gain of SHB is a by-product of mini-batching. We substantiate this claim by showing that SHB can obtain an accelerated rate when the mini-batch size is larger than some threshold. In particular, for strongly-convex quadratics with condition number $\kappa$, we prove that SHB with the standard step-size and momentum parameters results in an $O\left(\exp(-\frac{T}{\sqrt{\kappa}}) + \sigma \right)$ convergence rate, where $T$ is the number of iterations and $\sigma^2$ is the variance in the stochastic gradients. To ensure convergence to the minimizer, we propose a multi-stage approach that results in a noise-adaptive $O\left(\exp\left(-\frac{T}{\sqrt{\kappa}} \right) + \frac{\sigma}{T}\right)$ rate. For general strongly-convex functions, we use the averaging interpretation of SHB along with exponential step-sizes to prove an $O\left(\exp\left(-\frac{T}{\kappa} \right) + \frac{\sigma^2}{T} \right)$ convergence to the minimizer in a noise-adaptive manner. Finally, we empirically demonstrate the effectiveness of the proposed algorithms.

Decision-Aware Actor-Critic with Function Approximation and Theoretical Guarantees

Actor-critic (AC) methods are widely used in reinforcement learning (RL) and benefit from the flexibility of using any policy gradient method as the actor and value-based method as the critic. The critic is usually trained by minimizing the TD error, an objective that is potentially decorrelated with the true goal of achieving a high reward with the actor. We address this mismatch by designing a joint objective for training the actor and critic in a decision-aware fashion. We use the proposed objective to design a generic, AC algorithm that can easily handle any function approximation. We explicitly characterize the conditions under which the resulting algorithm guarantees monotonic policy improvement, regardless of the choice of the policy and critic parameterization. Instantiating the generic algorithm results in an actor that involves maximizing a sequence of surrogate functions (similar to TRPO, PPO) and a critic that involves minimizing a closely connected objective. Using simple bandit examples, we provably establish the benefit of the proposed critic objective over the standard squared error. Finally, we empirically demonstrate the benefit of our decision-aware actor-critic framework on simple RL problems.

Target-based Surrogates for Stochastic Optimization

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a target space (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the $SSO$ algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for $SSO$ when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of $SSO$.