wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We propose two variants of  envy-freeness up to one item for the weighted setting: in the strong variant, the  envy can be eliminated by removing an item from the envied agent's bundle , whereas in the weak variant,  envy can be eliminated by either removing an item from the envied agent's bundle or by replicating an item from the envied agent's bundle in the envying agent's bundle  .
Revised:  We propose two variants of envy-freeness up to one item for the weighted setting: in the strong variant, the envy can be eliminated by removing an item from the envied agent's bundle , whereas in the weak variant,weak envy can be eliminated by either removing an item from the envied agent's bundle or by replicating an item from the envied agent's bundle in the envying agent's bundle .
Edit intent: fluency
Original:  We propose two variants of  envy-freeness up to one item for the weighted setting: in the strong variant, the  envy can be eliminated by removing an item from the envied agent's bundle , whereas in the weak variant,  envy can be eliminated by either removing an item from the envied agent's bundle or by replicating an item from the envied agent's bundle in the envying agent's bundle  .
Revised:  We propose two variants of envy-freeness up to one item for the weighted setting: in the strong variant, the envy can be eliminated by removing an item from the envied agent's bundle , whereas in the weak variant, (where the envy can be eliminated by either removing an item from the envied agent's bundle or by replicating an item from the envied agent's bundle in the envying agent's bundle .
Edit intent: clarity
Original:  We propose two variants of  envy-freeness up to one item for the weighted setting: in the strong variant, the  envy can be eliminated by removing an item from the envied agent's bundle , whereas in the weak variant,  envy can be eliminated by either removing an item from the envied agent's bundle or by replicating an item from the envied agent's bundle in the envying agent's bundle  .
Revised:  We propose two variants of envy-freeness up to one item for the weighted setting: in the strong variant, the envy can be eliminated by removing an item from the envied agent's bundle , whereas in the weak variant, envy can be eliminated either by removing an item from the envied agent's bundle or by replicating an item from the envied agent's bundle in the envying agent's bundle .
Edit intent: fluency
Original:  We propose two variants of  envy-freeness up to one item for the weighted setting: in the strong variant, the  envy can be eliminated by removing an item from the envied agent's bundle , whereas in the weak variant,  envy can be eliminated by either removing an item from the envied agent's bundle or by replicating an item from the envied agent's bundle in the envying agent's bundle  .
Revised:  We propose two variants of envy-freeness up to one item for the weighted setting: in the strong variant, the envy can be eliminated by removing an item from the envied agent's bundle , whereas in the weak variant, envy can be eliminated by either removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envying agent's bundle .
Edit intent: clarity
Original:  We propose two variants of  envy-freeness up to one item for the weighted setting: in the strong variant, the  envy can be eliminated by removing an item from the envied agent's bundle , whereas in the weak variant,  envy can be eliminated by either removing an item from the envied agent's bundle or by replicating an item from the envied agent's bundle in the envying agent's bundle  .
Revised:  We propose two variants of envy-freeness up to one item for the weighted setting: in the strong variant, the envy can be eliminated by removing an item from the envied agent's bundle , whereas in the weak variant, envy can be eliminated by either removing an item from the envied agent's bundle or by replicating an item from the envied agent's bundle in the envious agent's bundle .
Edit intent: fluency
Original:  We propose two variants of  envy-freeness up to one item for the weighted setting: in the strong variant, the  envy can be eliminated by removing an item from the envied agent's bundle , whereas in the weak variant,  envy can be eliminated by either removing an item from the envied agent's bundle or by replicating an item from the envied agent's bundle in the envying agent's bundle  .
Revised:  We propose two variants of envy-freeness up to one item for the weighted setting: in the strong variant, the envy can be eliminated by removing an item from the envied agent's bundle , whereas in the weak variant, envy can be eliminated by either removing an item from the envied agent's bundle or by replicating an item from the envied agent's bundle in the envying agent's bundle ) .
Edit intent: fluency
Original:  We prove that for additive valuations, a strongly weighted envy-free allocation up to one item always existsand can be efficiently computed by means of a weight-based picking sequence . For two agents, we can also efficiently achieve strong weighted envy-freeness up to one item in conjunction with Pareto optimality using a weighted version of the classic adjusted winner algorithm.
Revised:  We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists; however, an allocation that maximizes the weighted Nash social welfare may not be strongly WEF1 but always satisfies the weak version of the property. Moreover, we establish that a generalization of the round-robin picking sequence produces in polynomial time a strongly WEF1 allocation for an arbitrary number of agents; for two agents, we can also efficiently achieve strong weighted envy-freeness up to one item in conjunction with Pareto optimality using a weighted version of the classic adjusted winner algorithm.
Edit intent: meaning-changed
Original:  We propose two variants of weighted envy-freeness up to one item (WEF1) --strong ( where the envy can be eliminated by removing an item from the envied agent's bundle ) andweak ( where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envious agent's bundle ) . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Revised:  We propose two variants of weighted envy-freeness up to one item (WEF1) strong ( where the envy can be eliminated by removing an item from the envied agent's bundle ) andweak ( where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envious agent's bundle ) . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Edit intent: fluency
Original:  We propose two variants of weighted envy-freeness up to one item (WEF1) --strong ( where the envy can be eliminated by removing an item from the envied agent's bundle ) andweak ( where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envious agent's bundle ) . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Revised:  We propose two variants of weighted envy-freeness up to one item (WEF1) -- ( where the envy can be eliminated by removing an item from the envied agent's bundle ) andweak ( where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envious agent's bundle ) . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Edit intent: fluency
Original:  We propose two variants of weighted envy-freeness up to one item (WEF1) --strong ( where the envy can be eliminated by removing an item from the envied agent's bundle ) andweak ( where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envious agent's bundle ) . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Revised:  We propose two variants of weighted envy-freeness up to one item (WEF1) --strong : strong, where the envy can be eliminated by removing an item from the envied agent's bundle ) andweak ( where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envious agent's bundle ) . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Edit intent: meaning-changed
Original:  We propose two variants of weighted envy-freeness up to one item (WEF1) --strong ( where the envy can be eliminated by removing an item from the envied agent's bundle ) andweak ( where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envious agent's bundle ) . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Revised:  We propose two variants of weighted envy-freeness up to one item (WEF1) --strong ( where the envy can be eliminated by removing an item from the envied agent's bundle weak ( where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envious agent's bundle ) . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Edit intent: coherence
Original:  We propose two variants of weighted envy-freeness up to one item (WEF1) --strong ( where the envy can be eliminated by removing an item from the envied agent's bundle ) andweak ( where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envious agent's bundle ) . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Revised:  We propose two variants of weighted envy-freeness up to one item (WEF1) --strong ( where the envy can be eliminated by removing an item from the envied agent's bundle ) and ( where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envious agent's bundle ) . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Edit intent: fluency
Original:  We propose two variants of weighted envy-freeness up to one item (WEF1) --strong ( where the envy can be eliminated by removing an item from the envied agent's bundle ) andweak ( where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envious agent's bundle ) . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Revised:  We propose two variants of weighted envy-freeness up to one item (WEF1) --strong ( where the envy can be eliminated by removing an item from the envied agent's bundle ) andweak , and weak, where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envious agent's bundle ) . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Edit intent: meaning-changed
Original:  We propose two variants of weighted envy-freeness up to one item (WEF1) --strong ( where the envy can be eliminated by removing an item from the envied agent's bundle ) andweak ( where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envious agent's bundle ) . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Revised:  We propose two variants of weighted envy-freeness up to one item (WEF1) --strong ( where the envy can be eliminated by removing an item from the envied agent's bundle ) andweak ( where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envying agent's bundle ) . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Edit intent: fluency
Original:  We propose two variants of weighted envy-freeness up to one item (WEF1) --strong ( where the envy can be eliminated by removing an item from the envied agent's bundle ) andweak ( where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envious agent's bundle ) . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Revised:  We propose two variants of weighted envy-freeness up to one item (WEF1) --strong ( where the envy can be eliminated by removing an item from the envied agent's bundle ) andweak ( where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envious agent's bundle . We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists;
Edit intent: fluency
Original:  for two agents, we can efficiently achieve both strong WEF1 and Pareto optimality by adapting the classic adjusted winner algorithm. We also explore the connections of WEF1 with approximations to the weighted versions of two other fairness concepts: proportionality and the maximin share guarantee .
Revised:  for two agents, we can efficiently achieve both strong WEF1 and Pareto optimality by adapting the adjusted winner procedure. Our work exhibits several aspects in which weighted fair division is richer and more challenging than its unweighted counterpart .
Edit intent: clarity
Original:  We propose two variants of weighted envy-freeness up to one item (WEF1): strong, where the envy can be eliminated by removing an item from the envied agent's bundle, and weak, where the envy can be eliminated either by removing an item  as in the strong version  or by replicating an item from the envied agent's bundle in the envying agent's bundle.
Revised:  We propose two variants of weighted envy-freeness up to one item (WEF1): strong, where envy can be eliminated by removing an item from the envied agent's bundle, and weak, where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envying agent's bundle.
Edit intent: fluency
Original:  We propose two variants of weighted envy-freeness up to one item (WEF1): strong, where the envy can be eliminated by removing an item from the envied agent's bundle, and weak, where the envy can be eliminated either by removing an item  as in the strong version  or by replicating an item from the envied agent's bundle in the envying agent's bundle.
Revised:  We propose two variants of weighted envy-freeness up to one item (WEF1): strong, where the envy can be eliminated by removing an item from the envied agent's bundle, and weak, where envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envying agent's bundle.
Edit intent: fluency
Original:  We propose two variants of weighted envy-freeness up to one item (WEF1): strong, where the envy can be eliminated by removing an item from the envied agent's bundle, and weak, where the envy can be eliminated either by removing an item  as in the strong version  or by replicating an item from the envied agent's bundle in the envying agent's bundle.
Revised:  We propose two variants of weighted envy-freeness up to one item (WEF1): strong, where the envy can be eliminated by removing an item from the envied agent's bundle, and weak, where the envy can be eliminated either by removing an item ( as in the strong version or by replicating an item from the envied agent's bundle in the envying agent's bundle.
Edit intent: fluency
Original:  We propose two variants of weighted envy-freeness up to one item (WEF1): strong, where the envy can be eliminated by removing an item from the envied agent's bundle, and weak, where the envy can be eliminated either by removing an item  as in the strong version  or by replicating an item from the envied agent's bundle in the envying agent's bundle.
Revised:  We propose two variants of weighted envy-freeness up to one item (WEF1): strong, where the envy can be eliminated by removing an item from the envied agent's bundle, and weak, where the envy can be eliminated either by removing an item as in the strong version ) or by replicating an item from the envied agent's bundle in the envying agent's bundle.
Edit intent: fluency
Original:  We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists ; however , an allocation that maximizes the weighted Nash social welfare may not be strongly WEF1  but always satisfies the weak version of the property.
Revised:  We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists and can be computed in pseudo-polynomial time; moreover , an allocation that maximizes the weighted Nash social welfare may not be strongly WEF1 but always satisfies the weak version of the property.
Edit intent: meaning-changed
Original:  The optimization of congruent formulations of the free energy functional (variational and expected) , in active inference , enables agents to make inferences about the environment and select optimal behaviors.
Revised:  This problem is also considered in reinforcement learning, but limited work exists on comparing the two approaches on the same discrete-state environments. In this paper, we provide: 1) an accessible overview of the discrete-state formulation of active inference, highlighting natural behaviors in active inference , enables agents to make inferences about the environment and select optimal behaviors.
Edit intent: meaning-changed
Original:  The optimization of congruent formulations of the free energy functional (variational and expected) , in active inference , enables agents to make inferences about the environment and select optimal behaviors. The agent achieves this by evaluating (sensory) evidence in relation to its internal generative model that entails beliefs about future (hidden) states and sequence of actions that it can choose. In contrast to analogous frameworks - by operating in a pure belief-based setting (free energy functional of beliefs about states) - active inference agents can carry out epistemic exploration and naturally account for uncertainty about their environment  .
Revised:  The optimization of congruent formulations of the free energy functional (variational and expected) , in active inference that are generally engineered in reinforcement learning; 2) to our knowledge, the first explicit discrete-state comparison between active inference and reinforcement learning on an OpenAI gym baseline. We begin by providing a condensed overview of the active inference literature, in particular viewing the various natural behaviors of active inference agents through the lens of reinforcement learning. We show that by operating in a pure belief-based setting (free energy functional of beliefs about states) - active inference agents can carry out epistemic exploration and naturally account for uncertainty about their environment .
Edit intent: meaning-changed
Original:  In contrast to analogous frameworks - by operating in a pure belief-based setting (free energy functional of beliefs about states) - active inference agents can carry out epistemic exploration and naturally account for uncertainty about their environment  .
Revised:  In contrast to analogous frameworks - by operating in a pure belief-based setting (free energy functional of beliefs about states) - active inference agents can carry out epistemic exploration - and account for uncertainty about their environment .
Edit intent: clarity
Original:  In contrast to analogous frameworks - by operating in a pure belief-based setting (free energy functional of beliefs about states) - active inference agents can carry out epistemic exploration and naturally account for uncertainty about their environment  .
Revised:  In contrast to analogous frameworks - by operating in a pure belief-based setting (free energy functional of beliefs about states) - active inference agents can carry out epistemic exploration and naturally account for uncertainty about their environment - in a Bayes optimal fashion. We make these properties explicit by showing that the active inference agent's ability to carry out online planning, in a pure-belief setting, enables it to act optimally, given the non-stationary dynamics of an environment when compared to both Q-learning and Bayesian model-based reinforcement learning agents .
Edit intent: meaning-changed
Original:  Through this review, we disambiguate these properties , by providing a condensed overview of the theory underpinning active inference . A T-maze simulation is used to demonstrate how these behaviors emerge naturally, as the agent makes inferences about the observed outcomes and optimizes its generative model (via belief updating). Additionally, the discrete state-space and time formulation presented provides an accessible guide on how to derive the (variational and expected) free energy equations and belief updating rules.
Edit intent: coherence
Original:  e.g., robotic arm movement, playing Atari games, etc., if appropriate underlying probability distributions (i.e. generative model) can be formulated  .
Revised:  e.g., robotic arm movement, playing Atari games, etc., if appropriate underlying probability distributions (i.e. generative model) can be formulated . In short, we aim to demystify the behavior of active inference agents by presenting an accessible discrete state-space and time formulation, and demonstrate these behaviors in a OpenAI gym environment, alongside reinforcement learning agents .
Edit intent: meaning-changed
Original:  We show that by operating in a pure belief-based setting, active inference agents can carry out epistemic exploration - and account for uncertainty about their environment - in a Bayes optimal fashion.
Revised:  We show that by operating in a pure belief-based setting, active inference agents can carry out epistemic exploration - and account for uncertainty about their environment in a Bayes-optimal fashion. Furthermore, we show that the reliance on an explicit reward signal in RL is removed in active inference, where reward can simply be treated as another observation; even in the total absence of rewards, agent behaviors are learned through preference learning.
Edit intent: meaning-changed
Original:  We make these properties explicit by showing that the active inference agent's ability to carry out online planning, in a pure-belief setting, enables it to act optimally, given the non-stationary dynamics of an environment when compared to both Q-learning and Bayesian model-based reinforcement learning agents .
Revised:  We make these properties explicit by showing two scenarios in which active inference agents can infer behaviors in reward-free environments compared to both Q-learning and Bayesian model-based reinforcement learning agents .
Edit intent: clarity