Q-based Variational Inverse Reinforcement Learning

The development of safe and beneficial AI requires that systems can learn and act in accordance with human preferences. However, explicitly specifying these preferences by hand is often infeasible. Inverse reinforcement learning (IRL) addresses this challenge by inferring preferences, represented as reward functions, from expert behaviour. We introduce Q-based Variational IRL (QVIRL), a novel Bayesian IRL method that recovers a posterior distribution over rewards from expert demonstrations via primarily learning a variational distribution over optimal Q-values. Unlike previous approaches, QVIRL combines scalability with uncertainty quantification, important for safety-critical applications as well as active learning. We demonstrate QVIRL's strong performance in apprenticeship learning across various tasks, including gridworlds, Lunar Lander, the Highway Environment, and two ATARI games both with static expert data and with active learning. It is the first method for Bayesian IRL that demonstrates training from raw pixel observations.

Efficient Hypergradient Descent for Inverse Reinforcement Learning

Inverse reinforcement learning (IRL) aims to recover a reward function under which the resulting policy reproduces the behavior observed in expert demonstrations. A natural approach is to formulate IRL as a bilevel optimization problem, in which the inner level corresponds to policy optimization under the learned reward and the outer level measures the discrepancy between the induced policy and expert data. However, this formulation is computationally challenging in practice because the outer update requires a hypergradient involving an inverse-Hessian-vector product for the inner objective. We address this challenge by showing that, at the inner optimum, the Hessian of the inner objective is proportional to the Fisher information matrix of the policy, yielding a structured Fisher-based hypergradient closely related to Natural Hypergradient Descent. To address the resulting scalability bottleneck associated with large Fisher matrices, we approximate the required inverse-Fisher-vector product using a streaming spectral sketch, avoiding explicit construction of the Fisher matrix. We evaluate our approach against a first-order stochastic bilevel baseline across discrete- and continuous-control environments. The results demonstrate competitive policy performance and strong reward-ranking quality, while Fisher sketching reduces curvature-storage complexity and can improve computational efficiency relative to an explicit Fisher solver.

From Optimal Actions to World Models: Identifiability of Transition Kernels in Discounted MDPs

We study what can be recovered about the transition probabilities of a Markov decision process from optimal actions alone. This is closely related to the inverse problem considered by Letcher et al., who ask when the dynamics can be recovered from numerical \(Q\)-values. Here the numerical values themselves are not observed; only the optimal actions are known, for every reward in a given class. For state-action rewards \(r(s,a)\), knowing the optimal actions for every reward also tells us how much better one action is than another when each is followed by the same fixed policy. This is still not enough to determine the transition probabilities uniquely. We prove that two kernels give the same optimal actions for every reward exactly when \[ Q_{s,a} = \Bigl(P_{s,a}+\tfrac1γe_s^{\mathsf T}(L-I)\Bigr)L^{-1} \] for one invertible matrix \(L\) satisfying \(L\mathbf 1=\mathbf 1\). Near a kernel with strictly positive entries, there is an \(n(n-1)\)-dimensional family of different kernels with this property. The result is unchanged if we consider only rewards having a unique optimal action at every state. We then compare this with rewards of the forms \(r(s)\) and \(r(s,a,s')\). Rewards that depend on the next state can usually recover the transition kernel itself: every row at a state with at least two actions is determined, and we describe exactly when a row at a state with one action can remain hidden. State rewards reveal less: two kernels give the same optimal actions exactly when every deterministic policy is optimal for the same set of rewards. The results show how the form of the reward affects what can be learned about the dynamics from optimal actions alone.

Does Latent Context Help? A Controlled Evaluation of Inverse Reinforcement Learning in Arctic Shipping

Artificial Intelligence (AI)-assisted navigation can help Arctic shipping adapt to rapidly changing sea-ice conditions, but reliable deployment requires reward models that are interpretable and robust to changing environments. Inverse reinforcement learning (IRL) provides a framework for recovering such rewards from vessel trajectories, while recent meta-IRL methods introduce latent context variables to capture behavioral heterogeneity. However, it remains unclear whether these latent representations recover genuinely hidden preferences or simply re-encode information already available in the observed state. We conduct a controlled evaluation on 3,186 AIS-derived voyages from 202 vessels across nine Arctic shipping seasons, comparing a linear shared reward, a nonlinear shared reward, and a latent-context model built on the same nonlinear architecture. The nonlinear reward improves held-out likelihood by 50.9% over the linear baseline, whereas adding vessel-specific latent context reduces performance by 16.5%. Behavioral analysis, context probes, and a pre-registered feature-hiding ablation show that apparent vessel-level variation is largely explained by observable route and environmental conditions rather than hidden vessel-specific factors. Moreover, predictive accuracy, route fidelity, and reward transfer yield different model rankings, demonstrating that no single metric is sufficient to evaluate learned rewards. These findings motivate testing whether the observed route, environmental, and vessel features already explain behavioral variation before adding per-vessel latent context. This supports more trustworthy AI deployment in safety-critical domains.

Inverse RL Helps Align AI by Imitating Humans

Language model alignment aims to make model behavior reliably reflect desirable properties such as helpfulness, safety, and instruction following. Current approaches typically use supervised fine-tuning on demonstrations or reinforcement learning with rewards derived from verifiers or human feedback. These paradigms leave an important question underexplored: can demonstrations alone yield an implicit reward that can be inspected, reused, and optimized on-policy to align AI? Motivated by inverse reinforcement learning, we introduce Projected Alignment Reward Estimated from Demonstrations (PARED). PARED recovers the implicit reward underlying expert demonstrations as an explicit function over a small set of response-level features, learned by a lightweight discriminator that separates demonstrations from the policy's own samples in this feature space. Unlike a standard reward model, PARED requires no task-specific preference annotations: demonstrations provide the task-specific supervision, which can be augmented with AI feedback as additional dimensions of supervision. Through experiments involving inference-time reranking and adversarial on-policy RL, we show that the recovered reward improves a base policy without a supervised loss and yields further gains when optimized after standard supervised fine-tuning. Additionally, we demonstrate that PARED can be used for contextual alignment, in which a single policy can be tailored to the preferences of different audiences.

Generalize and Guide: Decomposing Rewards for Few-Shot Inverse Reinforcement Learning

Inverse reinforcement learning (IRL) provides a powerful framework for learning from demonstrations. However, real-world tasks often exhibit substantial natural variations (e.g., picking up mugs with varying shapes), making it impractical to collect demonstrations that fully specify a new task under every possible scenario. In practice, while demonstrations for the target task are limited, it is often easier to obtain datasets of heterogeneous but related behaviors. This motivates the problem of few-shot IRL with multi-task demonstrations (FM-IRL), where an agent must learn a new task with substantial variations from only a limited number of target-task demonstrations, together with sufficient demonstrations of related tasks and online agent experience. To do so, we must both recover the expert distribution of the new task and provide guidance when the agent deviates from it. We introduce Multitask discriminator Proximity-Guided IRL (MPG), which learns two complementary reward components: (1) a generalizable discriminator that transfers shared structure across related tasks to identify expert behavior in a new task, and (2) a proximity function that measures how far a state deviates from expert behavior and provides corrective guidance during exploration. We demonstrate the effectiveness of our method on multiple challenging navigation and manipulation tasks under significant variations (e.g., object configurations, table layouts, and initial robot poses), achieving an average success rate of 81.2%, outperforming the strongest per-task baseline by an average of 24.7 percentage points.

A Noise-Robust Elicit-to-Optimize Framework for Distortion Riskmetrics via Inverse Reinforcement Learning

We propose a noise-robust elicit-to-optimize framework that integrates inverse reinforcement learning (IRL) and reinforcement learning (RL) for eliciting agents' risk preferences and optimizing policies under a broad class of risk objectives characterized by distortion riskmetrics. On the elicitation side, we propose an adaptive Bayesian IRL method that infers agents' latent risk objectives from their noisy observed decisions, explicitly allowing agents to take stochastic and suboptimal actions. We establish the existence of a finite set of distinguishing questions that identifies the preferred distortion riskmetric within the candidate class and prove that the convergence rate of the algorithm is of order $O(\exp(-cm+O(\sqrt{m\log m})))$ under general settings, where $c>0$ is a constant and $m$ denotes the number of algorithm iterations. On the optimization side, we develop a model-free RL algorithm for optimizing policies under conditional distortion riskmetrics. By representing the objective as an integral of the conditional cost quantile function with respect to the distortion function, the method unifies distortion-riskmetric objectives. We optimize diverse risk objectives by extending the Proximal Policy Optimization (PPO) algorithm with policy, value, and quantile neural networks, where the quantile network estimates the full conditional cost quantile function and enables numerical evaluation of general risk objectives. A comprehensive empirical study demonstrates the framework's elicitation accuracy and effectiveness in complex financial environments.

Nonparametric Bayesian Inverse Reinforcement Learning with Data-Parallel Gibbs Sampling

Inverse Reinforcement Learning recovers reward functions from expert demonstrations, but standard formulations assume that all demonstrations come from a single expert. When demonstrations are pooled from multiple experts with distinct preferences, parametric methods recover an averaged reward that fits no individual expert well. We implement Nonparametric Bayesian Inverse Reinforcement Learning with a Dirichlet Process prior over reward functions, allowing the number of latent reward types to be inferred jointly with the rewards themselves. Inference uses a collapsed Gibbs sampler combining a Chinese Restaurant Process update for cluster assignments with a Metropolis-Hastings update for reward weights, and soft value iteration as the inner planning routine. We evaluate on a 10x10 ObjectWorld grid with two and three ground-truth reward types. The serial sampler recovers K=2 with Adjusted Rand Index of 1.000, substantially outperforming a Maximum Entropy IRL baseline (ARI=0.000). Extension to K=3 shows that the sampler correctly identifies the number of clusters in all runs; assignment ARI of 0.48-0.58 reflects behavioral overlap between expert types that persists across grid instantiations, revealing that reliable K=3 evaluation on ObjectWorld requires controlled object placement rather than random seeding. We further parallelize the sampler across CPU cores using Ray on HPC hardware, achieving a peak speedup of 4.79x at 8 workers, and characterize a throughput-versus-accuracy tradeoff arising from the consensus merge heuristic used during state aggregation. Code and a containerized environment are available at https://github.com/dasashreeya/np_bayes_irl.

Multi-Modal, Multi-Environment Machine Teaching for Robust Reward Learning

As autonomous agents are increasingly deployed across diverse operational contexts, aligning their behavior with human intent demands reward functions that remain robust to such changes rather than overfitting to any single environment. Inverse reinforcement learning (IRL) provides a principled way to infer such objectives from human feedback. However, existing analyses of optimal teaching approaches for IRL focus on single-environment, demonstration-only settings, leaving underexplored how heterogeneous feedback modalities and environment dynamics jointly constrain reward functions that generalize across multiple environments. Because demonstrations in one MDP entangle reward information with that environments specific structure, the resulting rewards frequently fail to generalize when the agent is deployed in a new setting. We first analyze how different feedback modalities constrain rewards, showing that, in the unlimited-data regime, comparisons impose strictly stronger global constraints than other modalities. Beyond this theoretical analysis, we introduce a hierarchical machine teaching algorithm for reward learning that operates across multiple MDPs. The algorithm first greedily selects informative environments that expose complementary reward constraints, then strategically queries low-cost feedback within those environments. Empirically, our method achieves substantially lower regret and stronger generalization to held-out environments than uniform teaching baselines under identical feedback budgets, demonstrating the importance of multi-environment, multi-modal teaching for learning dynamics-robust reward functions.

Maximum Entropy Inverse Reinforcement Learning for Mean-Field Games with Average Reward

We study inverse reinforcement learning for discrete-time, infinite-horizon mean-field games (MFGs) under an average-reward criterion. Expert demonstrations are assumed to arise from a stationary mean-field equilibrium under an unknown reward, and the goal is to recover a policy explaining the observed behaviour via the maximum causal entropy principle. We formulate the inverse problem by enforcing consistency with the expert mean-field term and long-run feature expectations, treating two reward classes within a unified occupation-measure framework. For finite-dimensional linear rewards, we give a convex dual reformulation with an explicit log-partition objective, and prove smoothness and curvature properties justifying constant-step-size gradient descent. For infinite-dimensional RKHS rewards, we develop a Lagrangian relaxation whose inner-maximising policy is characterised by a soft Bellman equation. The main obstacle is the absence of a discount-factor contraction. We resolve this by introducing a minorisation-based sub-stochastic kernel that yields a strict contraction of the soft Bellman operator. We establish Fréchet differentiability and Lipschitz smoothness of the log-likelihood score, leading to a gradient ascent algorithm with convergence guarantees. Two numerical examples, a malware-spread MFG and an RKHS-based consumer-choice model, show that the recovered policies closely match expert behaviour.

ConTraIRL: Factorized Contrastive Abstractions for Transferable IRL

Reward transfer in Inverse Reinforcement Learning (IRL) is unreliable when policies must generalize to unseen combinations of environment dynamics and task goals. We propose Factorized Contrastive Abstractions for Transferable IRL (ConTraIRL), a framework that enables compositional reward transfer by learning decoupled latent representations of these two factors. ConTraIRL uses a dual-encoder architecture that maps observations into separate dynamics and goal latent spaces, trained with a dual contrastive objective. Temporal alignment encourages the dynamics encoder to learn goal-invariant structure, while the goal encoder captures dynamics-invariant features. This factorization supports reward inference under recombined dynamics-goal settings. Experiments on continuous control benchmarks demonstrate effective few-shot transfer to unseen dynamics-goal pairings, improving sample efficiency and reward recovery over transfer IRL baselines.

Model-Free Inference of Investor Preferences: A Relative Entropy IRL Approach

We present a framework using Relative Entropy Inverse Reinforcement Learning (RE-IRL) to recover investor reward functions from observed investment actions and market conditions. Unlike traditional IRL algorithms, RE-IRL is employed to account for environments where transition probabilities are unknown or inaccessible. To address the challenge of data sparsity, we utilize a $K$-nearest neighbor approach to estimate the observed behavior policy. Furthermore, we propose a statistical testing framework to evaluate the validity and robustness of the estimated results.