Many decision-making problems feature multiple objectives. In such problems, it is not always possible to know the preferences of a decision-maker for different objectives. However, it is often possible to observe the behavior of decision-makers. In multi-objective decision-making, preference inference is the process of inferring the preferences of a decision-maker for different objectives. This research proposes a Dynamic Weight-based Preference Inference (DWPI) algorithm that can infer the preferences of agents acting in multi-objective decision-making problems, based on observed behavior trajectories in the environment. The proposed method is evaluated on three multi-objective Markov decision processes: Deep Sea Treasure, Traffic, and Item Gathering. The performance of the proposed DWPI approach is compared to two existing preference inference methods from the literature, and empirical results demonstrate significant improvements compared to the baseline algorithms, in terms of both time requirements and accuracy of the inferred preferences. The Dynamic Weight-based Preference Inference algorithm also maintains its performance when inferring preferences for sub-optimal behavior demonstrations. In addition to its impressive performance, the Dynamic Weight-based Preference Inference algorithm does not require any interactions during training with the agent whose preferences are inferred, all that is required is a trajectory of observed behavior.
Sequential decision making in the real world often requires finding a good balance of conflicting objectives. In general, there exist a plethora of Pareto-optimal policies that embody different patterns of compromises between objectives, and it is technically challenging to obtain them exhaustively using deep neural networks. In this work, we propose a novel multi-objective reinforcement learning (MORL) algorithm that trains a single neural network via policy gradient to approximately obtain the entire Pareto set in a single run of training, without relying on linear scalarization of objectives. The proposed method works in both continuous and discrete action spaces with no design change of the policy network. Numerical experiments in benchmark environments demonstrate the practicality and efficacy of our approach in comparison to standard MORL baselines.
We study a multi-objective multi-armed bandit problem in a dynamic environment. The problem portrays a decision-maker that sequentially selects an arm from a given set. If selected, each action produces a reward vector, where every element follows a piecewise-stationary Bernoulli distribution. The agent aims at choosing an arm among the Pareto optimal set of arms to minimize its regret. We propose a Pareto generic upper confidence bound (UCB)-based algorithm with change detection to solve this problem. By developing the essential inequalities for multi-dimensional spaces, we establish that our proposal guarantees a regret bound in the order of $\gamma_T\log(T/{\gamma_T})$ when the number of breakpoints $\gamma_T$ is known. Without this assumption, the regret bound of our algorithm is $\gamma_T\log(T)$. Finally, we formulate an energy-efficient waveform design problem in an integrated communication and sensing system as a toy example. Numerical experiments on the toy example and synthetic and real-world datasets demonstrate the efficiency of our policy compared to the current methods.
Many sequential decision-making problems need optimization of different objectives which possibly conflict with each other. The conventional way to deal with a multi-task problem is to establish a scalar objective function based on a linear combination of different objectives. However, for the case of having conflicting objectives with different scales, this method needs a trial-and-error approach to properly find proper weights for the combination. As such, in most cases, this approach cannot guarantee an optimal Pareto solution. In this paper, we develop a single-agent scale-independent multi-objective reinforcement learning on the basis of the Advantage Actor-Critic (A2C) algorithm. A convergence analysis is then done for the devised multi-objective algorithm providing a convergence-in-mean guarantee. We then perform some experiments over a multi-task problem to evaluate the performance of the proposed algorithm. Simulation results show the superiority of developed multi-objective A2C approach against the single-objective algorithm.
Multi-objective reinforcement learning (MORL) algorithms tackle sequential decision problems where agents may have different preferences over (possibly conflicting) reward functions. Such algorithms often learn a set of policies (each optimized for a particular agent preference) that can later be used to solve problems with novel preferences. We introduce a novel algorithm that uses Generalized Policy Improvement (GPI) to define principled, formally-derived prioritization schemes that improve sample-efficient learning. They implement active-learning strategies by which the agent can (i) identify the most promising preferences/objectives to train on at each moment, to more rapidly solve a given MORL problem; and (ii) identify which previous experiences are most relevant when learning a policy for a particular agent preference, via a novel Dyna-style MORL method. We prove our algorithm is guaranteed to always converge to an optimal solution in a finite number of steps, or an $\epsilon$-optimal solution (for a bounded $\epsilon$) if the agent is limited and can only identify possibly sub-optimal policies. We also prove that our method monotonically improves the quality of its partial solutions while learning. Finally, we introduce a bound that characterizes the maximum utility loss (with respect to the optimal solution) incurred by the partial solutions computed by our method throughout learning. We empirically show that our method outperforms state-of-the-art MORL algorithms in challenging multi-objective tasks, both with discrete and continuous state and action spaces.
In this work we introduce reinforcement learning techniques for solving lexicographic multi-objective problems. These are problems that involve multiple reward signals, and where the goal is to learn a policy that maximises the first reward signal, and subject to this constraint also maximises the second reward signal, and so on. We present a family of both action-value and policy gradient algorithms that can be used to solve such problems, and prove that they converge to policies that are lexicographically optimal. We evaluate the scalability and performance of these algorithms empirically, demonstrating their practical applicability. As a more specific application, we show how our algorithms can be used to impose safety constraints on the behaviour of an agent, and compare their performance in this context with that of other constrained reinforcement learning algorithms.
We consider the problem of two active particles in 2D complex flows with the multi-objective goals of minimizing both the dispersion rate and the energy consumption of the pair. We approach the problem by means of Multi Objective Reinforcement Learning (MORL), combining scalarization techniques together with a Q-learning algorithm, for Lagrangian drifters that have variable swimming velocity. We show that MORL is able to find a set of trade-off solutions forming an optimal Pareto frontier. As a benchmark, we show that a set of heuristic strategies are dominated by the MORL solutions. We consider the situation in which the agents cannot update their control variables continuously, but only after a discrete (decision) time, $\tau$. We show that there is a range of decision times, in between the Lyapunov time and the continuous updating limit, where Reinforcement Learning finds strategies that significantly improve over heuristics. In particular, we discuss how large decision times require enhanced knowledge of the flow, whereas for smaller $\tau$ all a priori heuristic strategies become Pareto optimal.
IoT sensors, especially video cameras, are ubiquitously deployed around the world to perform a variety of computer vision tasks in several verticals including retail, healthcare, safety and security, transportation, manufacturing, etc. To amortize their high deployment effort and cost, it is desirable to perform multiple video analytics tasks, which we refer to as Analytical Units (AUs), off the video feed coming out of every camera. In this paper, we first show that in a multi-AU setting, changing the camera setting has disproportionate impact on different AUs performance. In particular, the optimal setting for one AU may severely degrade the performance for another AU, and further the impact on different AUs varies as the environmental condition changes. We then present Elixir, a system to enhance the video stream quality for multiple analytics on a video stream. Elixir leverages Multi-Objective Reinforcement Learning (MORL), where the RL agent caters to the objectives from different AUs and adjusts the camera setting to simultaneously enhance the performance of all AUs. To define the multiple objectives in MORL, we develop new AU-specific quality estimator values for each individual AU. We evaluate Elixir through real-world experiments on a testbed with three cameras deployed next to each other (overlooking a large enterprise parking lot) running Elixir and two baseline approaches, respectively. Elixir correctly detects 7.1% (22,068) and 5.0% (15,731) more cars, 94% (551) and 72% (478) more faces, and 670.4% (4975) and 158.6% (3507) more persons than the default-setting and time-sharing approaches, respectively. It also detects 115 license plates, far more than the time-sharing approach (7) and the default setting (0).
Many real-world continuous control problems are in the dilemma of weighing the pros and cons, multi-objective reinforcement learning (MORL) serves as a generic framework of learning control policies for different preferences over objectives. However, the existing MORL methods either rely on multiple passes of explicit search for finding the Pareto front and therefore are not sample-efficient, or utilizes a shared policy network for coarse knowledge sharing among policies. To boost the sample efficiency of MORL, we propose Q-Pensieve, a policy improvement scheme that stores a collection of Q-snapshots to jointly determine the policy update direction and thereby enables data sharing at the policy level. We show that Q-Pensieve can be naturally integrated with soft policy iteration with convergence guarantee. To substantiate this concept, we propose the technique of Q replay buffer, which stores the learned Q-networks from the past iterations, and arrive at a practical actor-critic implementation. Through extensive experiments and an ablation study, we demonstrate that with much fewer samples, the proposed algorithm can outperform the benchmark MORL methods on a variety of MORL benchmark tasks.
We study fair multi-objective reinforcement learning in which an agent must learn a policy that simultaneously achieves high reward on multiple dimensions of a vector-valued reward. Motivated by the fair resource allocation literature, we model this as an expected welfare maximization problem, for some nonlinear fair welfare function of the vector of long-term cumulative rewards. One canonical example of such a function is the Nash Social Welfare, or geometric mean, the log transform of which is also known as the Proportional Fairness objective. We show that even approximately optimal optimization of the expected Nash Social Welfare is computationally intractable even in the tabular case. Nevertheless, we provide a novel adaptation of Q-learning that combines nonlinear scalarized learning updates and non-stationary action selection to learn effective policies for optimizing nonlinear welfare functions. We show that our algorithm is provably convergent, and we demonstrate experimentally that our approach outperforms techniques based on linear scalarization, mixtures of optimal linear scalarizations, or stationary action selection for the Nash Social Welfare Objective.
In many risk-aware and multi-objective reinforcement learning settings, the utility of the user is derived from a single execution of a policy. In these settings, making decisions based on the average future returns is not suitable. For example, in a medical setting a patient may only have one opportunity to treat their illness. Making decisions using just the expected future returns -- known in reinforcement learning as the value -- cannot account for the potential range of adverse or positive outcomes a decision may have. Therefore, we should use the distribution over expected future returns differently to represent the critical information that the agent requires at decision time by taking both the future and accrued returns into consideration. In this paper, we propose two novel Monte Carlo tree search algorithms. Firstly, we present a Monte Carlo tree search algorithm that can compute policies for nonlinear utility functions (NLU-MCTS) by optimising the utility of the different possible returns attainable from individual policy executions, resulting in good policies for both risk-aware and multi-objective settings. Secondly, we propose a distributional Monte Carlo tree search algorithm (DMCTS) which extends NLU-MCTS. DMCTS computes an approximate posterior distribution over the utility of the returns, and utilises Thompson sampling during planning to compute policies in risk-aware and multi-objective settings. Both algorithms outperform the state-of-the-art in multi-objective reinforcement learning for the expected utility of the returns.
Multi-objective reinforcement learning (MORL) is a relatively new field which builds on conventional Reinforcement Learning (RL) to solve multi-objective problems. One of common algorithm is to extend scalar value Q-learning by using vector Q values in combination with a utility function, which captures the user's preference for action selection. This study follows on prior works, and focuses on what factors influence the frequency with which value-based MORL Q-learning algorithms learn the optimal policy for an environment with stochastic state transitions in scenarios where the goal is to maximise the Scalarised Expected Return (SER) - that is, to maximise the average outcome over multiple runs rather than the outcome within each individual episode. The analysis of the interaction between stochastic environment and MORL Q-learning algorithms run on a simple Multi-objective Markov decision process (MOMDP) Space Traders problem with different variant versions. The empirical evaluations show that well designed reward signal can improve the performance of the original baseline algorithm, however it is still not enough to address more general environment. A variant of MORL Q-Learning incorporating global statistics is shown to outperform the baseline method in original Space Traders problem, but remains below 100 percent effectiveness in finding the find desired SER-optimal policy at the end of training. On the other hand, Option learning is guarantied to converge to desired SER-optimal policy but it is not able to scale up to solve more complex problem in real-life. The main contribution of this thesis is to identify the extent to which the issue of noisy Q-value estimates impacts on the ability to learn optimal policies under the combination of stochastic environments, non-linear utility and a constant learning rate.
Multi-agent Reinforcement Learning (MARL) is a powerful tool for training autonomous agents acting independently in a common environment. However, it can lead to sub-optimal behavior when individual incentives and group incentives diverge. Humans are remarkably capable at solving these social dilemmas. It is an open problem in MARL to replicate such cooperative behaviors in selfish agents. In this work, we draw upon the idea of formal contracting from economics to overcome diverging incentives between agents in MARL. We propose an augmentation to a Markov game where agents voluntarily agree to binding transfers of reward, under pre-specified conditions. Our contributions are theoretical and empirical. First, we show that this augmentation makes all subgame-perfect equilibria of all Fully Observable Markov Games exhibit socially optimal behavior, given a sufficiently rich space of contracts. Next, we show that for general contract spaces, and even under partial observability, richer contract spaces lead to higher welfare. Hence, contract space design solves an exploration-exploitation tradeoff, sidestepping incentive issues. We complement our theoretical analysis with experiments. Issues of exploration in the contracting augmentation are mitigated using a training methodology inspired by multi-objective reinforcement learning: Multi-Objective Contract Augmentation Learning (MOCA). We test our methodology in static, single-move games, as well as dynamic domains that simulate traffic, pollution management and common pool resource management.
Multi-objective reinforcement learning (MORL) approaches have emerged to tackle many real-world problems with multiple conflicting objectives by maximizing a joint objective function weighted by a preference vector. These approaches find fixed customized policies corresponding to preference vectors specified during training. However, the design constraints and objectives typically change dynamically in real-life scenarios. Furthermore, storing a policy for each potential preference is not scalable. Hence, obtaining a set of Pareto front solutions for the entire preference space in a given domain with a single training is critical. To this end, we propose a novel MORL algorithm that trains a single universal network to cover the entire preference space scalable to continuous robotic tasks. The proposed approach, Preference-Driven MORL (PD-MORL), utilizes the preferences as guidance to update the network parameters. It also employs a novel parallelization approach to increase sample efficiency. We show that PD-MORL achieves up to 25% larger hypervolume for challenging continuous control tasks and uses an order of magnitude fewer trainable parameters compared to prior approaches.
Many real-world problems contain multiple objectives and agents, where a trade-off exists between objectives. Key to solving such problems is to exploit sparse dependency structures that exist between agents. For example, in wind farm control a trade-off exists between maximising power and minimising stress on the systems components. Dependencies between turbines arise due to the wake effect. We model such sparse dependencies between agents as a multi-objective coordination graph (MO-CoG). In multi-objective reinforcement learning a utility function is typically used to model a users preferences over objectives, which may be unknown a priori. In such settings a set of optimal policies must be computed. Which policies are optimal depends on which optimality criterion applies. If the utility function of a user is derived from multiple executions of a policy, the scalarised expected returns (SER) must be optimised. If the utility of a user is derived from a single execution of a policy, the expected scalarised returns (ESR) criterion must be optimised. For example, wind farms are subjected to constraints and regulations that must be adhered to at all times, therefore the ESR criterion must be optimised. For MO-CoGs, the state-of-the-art algorithms can only compute a set of optimal policies for the SER criterion, leaving the ESR criterion understudied. To compute a set of optimal polices under the ESR criterion, also known as the ESR set, distributions over the returns must be maintained. Therefore, to compute a set of optimal policies under the ESR criterion for MO-CoGs, we present a novel distributional multi-objective variable elimination (DMOVE) algorithm. We evaluate DMOVE in realistic wind farm simulations. Given the returns in real-world wind farm settings are continuous, we utilise a model known as real-NVP to learn the continuous return distributions to calculate the ESR set.
We study policy optimization for Markov decision processes (MDPs) with multiple reward value functions, which are to be jointly optimized according to given criteria such as proportional fairness (smooth concave scalarization), hard constraints (constrained MDP), and max-min trade-off. We propose an Anchor-changing Regularized Natural Policy Gradient (ARNPG) framework, which can systematically incorporate ideas from well-performing first-order methods into the design of policy optimization algorithms for multi-objective MDP problems. Theoretically, the designed algorithms based on the ARNPG framework achieve $\tilde{O}(1/T)$ global convergence with exact gradients. Empirically, the ARNPG-guided algorithms also demonstrate superior performance compared to some existing policy gradient-based approaches in both exact gradients and sample-based scenarios.
In multi-objective optimization, learning all the policies that reach Pareto-efficient solutions is an expensive process. The set of optimal policies can grow exponentially with the number of objectives, and recovering all solutions requires an exhaustive exploration of the entire state space. We propose Pareto Conditioned Networks (PCN), a method that uses a single neural network to encompass all non-dominated policies. PCN associates every past transition with its episode's return. It trains the network such that, when conditioned on this same return, it should reenact said transition. In doing so we transform the optimization problem into a classification problem. We recover a concrete policy by conditioning the network on the desired Pareto-efficient solution. Our method is stable as it learns in a supervised fashion, thus avoiding moving target issues. Moreover, by using a single network, PCN scales efficiently with the number of objectives. Finally, it makes minimal assumptions on the shape of the Pareto front, which makes it suitable to a wider range of problems than previous state-of-the-art multi-objective reinforcement learning algorithms.
Infectious disease outbreaks can have a disruptive impact on public health and societal processes. As decision making in the context of epidemic mitigation is hard, reinforcement learning provides a methodology to automatically learn prevention strategies in combination with complex epidemic models. Current research focuses on optimizing policies w.r.t. a single objective, such as the pathogen's attack rate. However, as the mitigation of epidemics involves distinct, and possibly conflicting criteria (i.a., prevalence, mortality, morbidity, cost), a multi-objective approach is warranted to learn balanced policies. To lift this decision-making process to real-world epidemic models, we apply deep multi-objective reinforcement learning and build upon a state-of-the-art algorithm, Pareto Conditioned Networks (PCN), to learn a set of solutions that approximates the Pareto front of the decision problem. We consider the first wave of the Belgian COVID-19 epidemic, which was mitigated by a lockdown, and study different deconfinement strategies, aiming to minimize both COVID-19 cases (i.e., infections and hospitalizations) and the societal burden that is induced by the applied mitigation measures. We contribute a multi-objective Markov decision process that encapsulates the stochastic compartment model that was used to inform policy makers during the COVID-19 epidemic. As these social mitigation measures are implemented in a continuous action space that modulates the contact matrix of the age-structured epidemic model, we extend PCN to this setting. We evaluate the solution returned by PCN, and observe that it correctly learns to reduce the social burden whenever the hospitalization rates are sufficiently low. In this work, we thus show that multi-objective reinforcement learning is attainable in complex epidemiological models and provides essential insights to balance complex mitigation policies.
In real-world decision optimization, often multiple competing objectives must be taken into account. Following classical reinforcement learning, these objectives have to be combined into a single reward function. In contrast, multi-objective reinforcement learning (MORL) methods learn from vectors of per-objective rewards instead. In the case of multi-policy MORL, sets of decision policies for various preferences regarding the conflicting objectives are optimized. This is especially important when target preferences are not known during training or when preferences change dynamically during application. While it is, in general, straightforward to extend a single-objective reinforcement learning method for MORL based on linear scalarization, solutions that are reachable by these methods are limited to convex regions of the Pareto front. Non-linear MORL methods like Thresholded Lexicographic Ordering (TLO) are designed to overcome this limitation. Generalized MORL methods utilize function approximation to generalize across objective preferences and thereby implicitly learn multiple policies in a data-efficient manner, even for complex decision problems with high-dimensional or continuous state spaces. In this work, we propose \textit{generalized Thresholded Lexicographic Ordering} (gTLO), a novel method that aims to combine non-linear MORL with the advantages of generalized MORL. We introduce a deep reinforcement learning realization of the algorithm and present promising results on a standard benchmark for non-linear MORL and a real-world application from the domain of manufacturing process control.
Staged rollout is a strategy of incrementally releasing software updates to portions of the user population in order to accelerate defect discovery without incurring catastrophic outcomes such as system wide outages. Some past studies have examined how to quantify and automate staged rollout, but stop short of simultaneously considering multiple product or process metrics explicitly. This paper demonstrates the potential to automate staged rollout with multi-objective reinforcement learning in order to dynamically balance stakeholder needs such as time to deliver new features and downtime incurred by failures due to latent defects.