Optimal policies in standard MDPs can be obtained using either value iteration or policy iteration. However, in the case of zero-sum Markov games, there is no efficient policy iteration algorithm; e.g., it has been shown that one has to solve Omega(1/(1-alpha)) MDPs, where alpha is the discount factor, to implement the only known convergent version of policy iteration. Another algorithm, called naive policy iteration, is easy to implement but is only provably convergent under very restrictive assumptions. Prior attempts to fix naive policy iteration algorithm have several limitations. Here, we show that a simple variant of naive policy iteration for games converges exponentially fast. The only addition we propose to naive policy iteration is the use of lookahead policies, which are anyway used in practical algorithms. We further show that lookahead can be implemented efficiently in the function approximation setting of linear Markov games, which are the counterpart of the much-studied linear MDPs. We illustrate the application of our algorithm by providing bounds for policy-based RL (reinforcement learning) algorithms. We extend the results to the function approximation setting.

Open ad hoc teamwork is the problem of training a single agent to efficiently collaborate with an unknown group of teammates whose composition may change over time. A variable team composition creates challenges for the agent, such as the requirement to adapt to new team dynamics and dealing with changing state vector sizes. These challenges are aggravated in real-world applications in which the controlled agent only has a partial view of the environment. In this work, we develop a class of solutions for open ad hoc teamwork under full and partial observability. We start by developing a solution for the fully observable case that leverages graph neural network architectures to obtain an optimal policy based on reinforcement learning. We then extend this solution to partially observable scenarios by proposing different methodologies that maintain belief estimates over the latent environment states and team composition. These belief estimates are combined with our solution for the fully observable case to compute an agent's optimal policy under partial observability in open ad hoc teamwork. Empirical results demonstrate that our solution can learn efficient policies in open ad hoc teamwork in fully and partially observable cases. Further analysis demonstrates that our methods' success is a result of effectively learning the effects of teammates' actions while also inferring the inherent state of the environment under partial observability.

This paper endeavors to augment the robustness of offline reinforcement learning (RL) in scenarios laden with heavy-tailed rewards, a prevalent circumstance in real-world applications. We propose two algorithmic frameworks, ROAM and ROOM, for robust off-policy evaluation (OPE) and offline policy optimization (OPO), respectively. Central to our frameworks is the strategic incorporation of the median-of-means method with offline RL, enabling straightforward uncertainty estimation for the value function estimator. This not only adheres to the principle of pessimism in OPO but also adeptly manages heavy-tailed rewards. Theoretical results and extensive experiments demonstrate that our two frameworks outperform existing methods on the logged dataset exhibits heavy-tailed reward distributions.

Consider learning a decision support assistant to serve as an intermediary between (oracle) expert behavior and (imperfect) human behavior: At each time, the algorithm observes an action chosen by a fallible agent, and decides whether to *accept* that agent's decision, *intervene* with an alternative, or *request* the expert's opinion. For instance, in clinical diagnosis, fully-autonomous machine behavior is often beyond ethical affordances, thus real-world decision support is often limited to monitoring and forecasting. Instead, such an intermediary would strike a prudent balance between the former (purely prescriptive) and latter (purely descriptive) approaches, while providing an efficient interface between human mistakes and expert feedback. In this work, we first formalize the sequential problem of *online decision mediation* -- that is, of simultaneously learning and evaluating mediator policies from scratch with *abstentive feedback*: In each round, deferring to the oracle obviates the risk of error, but incurs an upfront penalty, and reveals the otherwise hidden expert action as a new training data point. Second, we motivate and propose a solution that seeks to trade off (immediate) loss terms against (future) improvements in generalization error; in doing so, we identify why conventional bandit algorithms may fail. Finally, through experiments and sensitivities on a variety of datasets, we illustrate consistent gains over applicable benchmarks on performance measures with respect to the mediator policy, the learned model, and the decision-making system as a whole.

Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent description of existing behavior in the first place. In this paper, we develop an expressive, unifying perspective on inverse decision modeling: a framework for learning parameterized representations of sequential decision behavior. First, we formalize the forward problem (as a normative standard), subsuming common classes of control behavior. Second, we use this to formalize the inverse problem (as a descriptive model), generalizing existing work on imitation/reward learning -- while opening up a much broader class of research problems in behavior representation. Finally, we instantiate this approach with an example (inverse bounded rational control), illustrating how this structure enables learning (interpretable) representations of (bounded) rationality -- while naturally capturing intuitive notions of suboptimal actions, biased beliefs, and imperfect knowledge of environments.

For a real-world decision-making problem, the reward function often needs to be engineered or learned. A popular approach is to utilize human feedback to learn a reward function for training. The most straightforward way to do so is to ask humans to provide ratings for state-action pairs on an absolute scale and take these ratings as reward samples directly. Another popular way is to ask humans to rank a small set of state-action pairs by preference and learn a reward function from these preference data. Recently, preference-based methods have demonstrated substantial success in empirical applications such as InstructGPT. In this work, we develop a theoretical comparison between these human feedback approaches in offline contextual bandits and show how human bias and uncertainty in feedback modelings can affect the theoretical guarantees of these approaches. Through this, our results seek to provide a theoretical explanation for the empirical successes of preference-based methods from a modeling perspective.

This paper considers a stochastic Multi-Armed Bandit (MAB) problem with dual objectives: (i) quick identification and commitment to the optimal arm, and (ii) reward maximization throughout a sequence of $T$ consecutive rounds. Though each objective has been individually well-studied, i.e., best arm identification for (i) and regret minimization for (ii), the simultaneous realization of both objectives remains an open problem, despite its practical importance. This paper introduces \emph{Regret Optimal Best Arm Identification} (ROBAI) which aims to achieve these dual objectives. To solve ROBAI with both pre-determined stopping time and adaptive stopping time requirements, we present an algorithm called EOCP and its variants respectively, which not only achieve asymptotic optimal regret in both Gaussian and general bandits, but also commit to the optimal arm in $\mathcal{O}(\log T)$ rounds with pre-determined stopping time and $\mathcal{O}(\log^2 T)$ rounds with adaptive stopping time. We further characterize lower bounds on the commitment time (equivalent to the sample complexity) of ROBAI, showing that EOCP and its variants are sample optimal with pre-determined stopping time, and almost sample optimal with adaptive stopping time. Numerical results confirm our theoretical analysis and reveal an interesting "over-exploration" phenomenon carried by classic UCB algorithms, such that EOCP has smaller regret even though it stops exploration much earlier than UCB, i.e., $\mathcal{O}(\log T)$ versus $\mathcal{O}(T)$, which suggests over-exploration is unnecessary and potentially harmful to system performance.

There are several theories in economics regarding the roots or causes of prosperity in a society. One of these theories or hypotheses -- named geography hypothesis -- mentions that the reason why some countries are prosperous and some others are poor is the geographical location of the countries in the world as makes their climate and environment favorable or unfavorable regarding natural resources. Another competing hypothesis states that man-made institutions particularly inclusive political institutions are the reasons why some countries are prosperous and some others are poor. On the other hand, there is a specific political theory developed for the long-term social development in Iran -- named Arbitrary Rule and Aridisolatic Society which particularly emphasizes on the role of aridity to shape arbitrary political and economical institutions in Iran, without any functional social classes in the society. In this paper, by extending the AI-Economist -- a recently developed two-level multi-agent reinforcement learning environment -- I show that when the central planner is ruling the environment by arbitrary rules, the society evolves through different paths in different environments. In the environment having band-like vertical isolated patches of natural resources, all mobile agents are equally exploited by the central planner and the central planner is also not gaining any income, while in the society having more uniformly distributed natural resources, the productivity and Maximin are higher and the society generates a heterogeneous stratified social structure. All these findings provide a partial answer to the above debate and reconcile the role of geography and political institutions on the long-term development in a region.

The ability to implement effective autonomous hypersonic strikes against an adversary can potentially change the balance of power for our forces located in proximity to a powerful adversary, significantly extending the depth of our defense. Hypersonic weapons have an advantage over slower missiles in that they both reduce the response time of a strike and are more difficult to intercept. The fastest response time for weapons deployed at large distances from the theater of operations would be achieved by boost-glide hypersonic strike weapons (HSW) or maneuverable ballistic re-entry vehicles (MBRV) launched on a depressed trajectory. Both approaches could be made more economical by launching multiple HSW or MBRV from a single rocket, similar to our approach with our nuclear deterrent. Hypersonic cruise missiles launched from strategic bombers would have slower response times, but may be more economical.

In reinforcement learning, off-policy evaluation (OPE) is the problem of estimating the expected return of an evaluation policy given a fixed dataset that was collected by running one or more different policies. One of the more empirically successful algorithms for OPE has been the fitted q-evaluation (FQE) algorithm that uses temporal difference updates to learn an action-value function, which is then used to estimate the expected return of the evaluation policy. Typically, the original fixed dataset is fed directly into FQE to learn the action-value function of the evaluation policy. Instead, in this paper, we seek to enhance the data-efficiency of FQE by first transforming the fixed dataset using a learned encoder, and then feeding the transformed dataset into FQE. To learn such an encoder, we introduce an OPE-tailored state-action behavioral similarity metric, and use this metric and the fixed dataset to learn an encoder that models this metric. Theoretically, we show that this metric allows us to bound the error in the resulting OPE estimate. Empirically, we show that other state-action similarity metrics lead to representations that cannot represent the action-value function of the evaluation policy, and that our state-action representation method boosts the data-efficiency of FQE and lowers OPE error relative to other OPE-based representation learning methods on challenging OPE tasks. We also empirically show that the learned representations significantly mitigate divergence of FQE under varying distribution shifts. Our code is available here: https://github.com/Badger-RL/ROPE.