A survey of multi-objective sequential decision-making

ArXiv, 2021

Real-world decision-making tasks are generally complex, requiring trade-offs between multiple, often conflicting, objectives. Despite this, the majority of research in reinforcement learning and decision-theoretic planning either assumes only a single objective, or that multiple objectives can be adequately handled via a simple linear combination. Such approaches may oversimplify the underlying problem and hence produce suboptimal results. This paper serves as a guide to the application of multi-objective methods to difficult problems, and is aimed at researchers who are already familiar with single-objective reinforcement learning and planning methods who wish to adopt a multi-objective perspective on their research, as well as practitioners who encounter multiobjective decision problems in practice. It identifies the factors that may influence the nature of the desired solution, and illustrates by example how these influence the design of multi-objective decision-making systems fo...

Neurocomputing

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Journal of Machine Learning Research, 2014

Many real-world problems involve the optimization of multiple, possibly conflicting objectives. Multi-objective reinforcement learning (MORL) is a generalization of standard reinforcement learning where the scalar reward signal is extended to multiple feedback signals, in essence, one for each objective. MORL is the process of learning policies that optimize multiple criteria simultaneously. In this paper, we present a novel temporal difference learning algorithm that integrates the Pareto dominance relation into a reinforcement learning approach. This algorithm is a multi-policy algorithm that learns a set of Pareto dominating policies in a single run. We name this algorithm Pareto Q-learning and it is applicable in episodic environments with deterministic as well as stochastic transition functions. A crucial aspect of Pareto Q-learning is the updating mechanism that bootstraps sets of Q-vectors. One of our main contributions in this paper is a mechanism that separates the expected immediate reward vector from the set of expected future discounted reward vectors. This decomposition allows us to update the sets and to exploit the learned policies consistently throughout the state space. To balance exploration and exploitation during learning, we also propose three set evaluation mechanisms. These three mechanisms evaluate the sets of vectors to accommodate for standard action selection strategies, such as-greedy. More precisely, these mechanisms use multi-objective evaluation principles such as the hypervolume measure, the cardinality indicator and the Pareto dominance relation to select the most promising actions. We experimentally validate the algorithm on multiple environments with two and three objectives and we demonstrate that Pareto Q-learning outperforms current state-of-the-art MORL algorithms with respect to the hypervolume of the obtained policies. We note that (1) Pareto Q-learning is able to learn the entire Pareto front under the usual assumption that each state-action pair is sufficiently sampled, while (2) not being biased by the shape of the Pareto front. Furthermore, (3) the set evaluation mechanisms provide indicative measures for local action selection and (4) the learned policies can be retrieved throughout the state and action space.

This paper describes a novel multi-objective reinforcement learning algorithm. The proposed algorithm first learns a model of the multi-objective sequential decision making problem, after which this learned model is used by a multiobjective dynamic programming method to compute Pareto optimal policies. The advantage of this model-based multi-objective reinforcement learning method is that once an accurate model has been estimated from the experiences of an agent in some environment, the dynamic programming method will compute all Pareto optimal policies. Therefore it is important that the agent explores the environment in an intelligent way by using a good exploration strategy. In this paper we have supplied the agent with two different exploration strategies and compare their effectiveness in estimating accurate models within a reasonable amount of time. The experimental results show that our method with the best exploration strategy is able to quickly learn all Pareto optimal policies for the Deep Sea Treasure problem.

2013 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL), 2013

In multi-objective problems, it is key to find compromising solutions that balance different objectives. The linear scalarization function is often utilized to translate the multiobjective nature of a problem into a standard, single-objective problem. Generally, it is noted that such as linear combination can only find solutions in convex areas of the Pareto front, therefore making the method inapplicable in situations where the shape of the front is not known beforehand, as is often the case. We propose a non-linear scalarization function, called the Chebyshev scalarization function, as a basis for action selection strategies in multi-objective reinforcement learning. The Chebyshev scalarization method overcomes the flaws of the linear scalarization function as it can (i) discover Pareto optimal solutions regardless of the shape of the front, i.e. convex as well as non-convex , (ii) obtain a better spread amongst the set of Pareto optimal solutions and (iii) is not particularly dependent on the actual weights used.

2016 IEEE 17th International Symposium on High Assurance Systems Engineering (HASE), 2016

Autonomous planning in safety critical systems is a difficult task where decisions must carefully balance optimisation for performance goals of the system while also keeping the system away from safety hazards. These tasks often conflict, and hence present a challenging multi-objective planning problem where at least one of the objectives relates to safety risk. Recasting safety risk into an objective introduces additional requirements on planning algorithms: safety risk cannot be "averaged out" nor can it be combined with other objectives without loss of information and losing its intended purpose as a tool in risk reduction. Thus, existing algorithms for multi-objective planning cannot be used directly as they do not provide any facility to accurately track and update safety risk. A common workaround is to restrict available decisions to those guaranteed safe a priori, but this can be overly conservative and hamper performance significantly. In this paper, we propose a planning algorithm based on multiobjective Monte-Carlo Tree Search to resolve these problems by recognising safety risk as a first class objective. Our algorithm explicitly models the safety of the system separately from the performance of the system, uses safety risk to both optimise and provide constraints for safety in the planning process, and uses an ALARP-based preference selection method to choose an appropriate safe plan from its output. The preference selection method chooses from the set of multiple safe plans to weigh risk against performance. We demonstrate the behaviour of the algorithm using an example representative of safety critical decision-making.

Many sequential decision-making problems require an agent to reason about both multiple objectives and uncertainty regarding the environment's state. Such problems can be naturally modelled as multi-objective partially observable Markov decision processes (MOPOMDPs). We propose optimistic linear support with alpha reuse (OLSAR), which computes a bounded approximation of the optimal solution set for all possible weightings of the objectives. The main idea is to solve a series of scalarized single-objective POMDPs, each corresponding to a different weighting of the objectives. A key insight underlying OLSAR is that the policies and value functions produced when solving scalarized POMDPs in earlier iterations can be reused to more quickly solve scalarized POMDPs in later iterations. We show experimentally that OLSAR outperforms, both in terms of runtime and approximation quality, alternative methods and a variant of OLSAR that does not leverage reuse.

Planning under uncertainty poses a complex problem in which multiple objectives often need to be balanced. When dealing with multiple objectives, it is often assumed that the relative importance of the objectives is known a priori. However, in practice human decision makers often find it hard to specify such preferences, and would prefer a decision support system that presents a range of possible alternatives. We propose two algorithms for computing these alternatives for the case of linearly weighted objectives. First, we propose an anytime method, approximate optimistic linear support (AOLS), that incrementally builds up a complete set of -optimal plans, exploiting the piecewise-linear and convex shape of the value function. Second, we propose an approximate anytime method, scalarised sample incremental improvement (SSII), that employs weight sampling to focus on the most interesting regions in weight space, as suggested by a prior over preferences. We show empirically that our methods are able to produce (near-)optimal alternative sets orders of magnitude faster than existing techniques.

2007

Abstract This paper describes a novel algorithm called CON-MODP for computing Pareto optimal policies for deterministic multi-objective sequential decision problems. CON-MODP is a value iteration based multi-objective dynamic programming algorithm that only computes stationary policies.

International Journal of Information Technology & Decision Making, 2013

A Markov decision process (MDP) is a general model for solving planning problems under uncertainty. It has been extended to multiobjective MDP to address multicriteria or multiagent problems in which the value of a decision must be evaluated according to several viewpoints, sometimes conflicting. Although most of the studies concentrate on the determination of the set of Pareto-optimal policies, we focus here on a more specialized problem that concerns the direct determination of policies achieving well-balanced tradeoffs. To this end, we introduce a reference point method based on the optimization of a weighted ordered weighted average (WOWA) of individual disachievements. We show that the resulting notion of optimal policy does not satisfy the Bellman principle and depends on the initial state. To overcome these difficulties, we propose a solution method based on a linear programming (LP) reformulation of the problem. Finally, we illustrate the feasibility of the proposed method o...