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The Soft Constraints Hypothesis: A Rational Analysis Approach to Resource…

- - - - i. Cost-benefit considerations provide a soft constraint on selection as they may be overridden by factors such as training or by deliberately adopted top-down strategies.
      - ii. Rather, the soft constraints hypothesis predicts optimal performance only in tasks where maximizing the expected gains and minimizing the expected costs of interactive routines (i.e., over 1/3 to 3 sec) is congruent with an optimal strategy at the global task level.
      - iii. This focus on local optimization is consistent with the rational analysis position that “Specifying the computational constraints essentially amounts to defining the locality over which the optimization is defined”
      - iv. In summary, the soft constraints hypothesis applies the rational analysis (Anderson, 1990, 1991) approach to the allocation of cognitive, perceptual, and motor resources for interactive behavior.
      - v. In this paper we seek to strengthen the soft constraints hypothesis by showing that its predictions are supported by empirical data and that an Ideal Performer Model, which enforces a strict temporal cost-benefit accounting, fits the empirical results.
    - - i. In contrast to the soft constraints hypothesis, alternative views of embodied cognition suggest that cognitive resources are conserved by biases that favor the use of perceptual motor resources
      - ii. An attraction of the minimum memory hypothesis is that it offers a simple heuristic for governing behavior, and unlike the soft constraints hypothesis, does not require an accounting of costs sensitive at the level of hundreds of milliseconds.
      - iii. The minimum memory hypothesis seems to embrace a limited capacity view of memory in which capacity is defined either by the number of slots available in a short-term or working memory buffer (Miller, 1956) or a limit on the amount of activation available to that buffer
      - iv. The soft constraints hypothesis implies that on the memory side of the tradeoff between interaction-intensive and memory-intensive strategies, the only factors that matter are the time required to encode, the time required to retrieve an item from memory, and the probability that an encoded item can be retrieved (i.e., is not forgotten) when needed.
      - v. Ballard and colleagues report that participants preferred an interaction-intensive strategy in which they would look at the Target Window first to encode a block’s color, get a block of that color from the Resource Window, look again at the Target Window to encode the block’s location, then move to the Workspace Window to place the block.
      - vi. They report that the interactionintensive strategy of looking twice took 3 s to execute, whereas the more memory-intensive strategy of encoding color and location at the same glance took 1.5 s to execute. They comment that “It is surprising that participants choose minimal memory strategies in view of their temporal cost”
      - v. Although this dramatic bias toward perceptual-motor access costs seems to support the minimum memory hypothesis, the study that Ballard and colleagues report contains a potential confound.
      - vi. The differential use of the two strategies at different phases of construction raises the question of whether the cost of encoding required by the memory-intensive strategy was paid at the end of the trial, as Ballard seems to assume, or whether it was amortized over the entire trial.
      - vii. Rather than obtaining perfect information from in-the-world as they needed it, both the Free-Access and Gray-Box groups preferred to rely on knowledge in-the-head.
      - viii. Unfortunately, this knowledge was obtained in the course of programming a show and, as the data suggest, was not as well learned as that obtained by the Memory-Test group.
      - ix. Unfortunately, neither Ballard’s study nor ours directly compared minimal memory with the soft constraints hypothesis.
      - x. In the work presented here, we attempt to show that differences of several hundreds of milliseconds are enough to shift the allocation of the resources used for interactive behavior from more interaction intensive to more memory intensive.
      - xi. Hence, in contrast to the minimum memory hypothesis, soft constraints posits that the control system is indifferent to the source of the resources it uses and is sensitive only to their expected utility as measured in time.
    - - i. Both the minimum memory hypothesis and soft constraints hypothesis present theories for the functional mechanism underlying the selection of low-level, interactive routines.
      - ii. The minimum memory hypothesis does not deny that effort is an important factor in deciding the mix of resources brought to bear on interactive behavior. It merely asserts that, all else equal, the control system is biased to expend perceptual-motor resources to conserve memory resources. Unfortunately, it is difficult for an empirical approach to determine when “all else” is equal.
      - iii.In predicting human performance, Simon told us that it is vital to nail down the “side conditions” such as “visual acuity, strength, shortterm memory, reaction times, and speed and limits of computation and reasoning”
      - iv.Hence, the first component is a detailed and accurate estimate of the constraints or “side conditions” that bounded rationality places on human performance
      - v. The second component is a computational or mathematical approach that is formally guaranteed to optimize temporal costs as opposed to any other metric.
      - vi. To conjoin these two key components (as well as several other necessary components) we combine elements of the ideal observer analysis approach from signal-detection theorists (Geisler, 2003; Macmillan & Creelman, 2004) with rational analysis (Anderson, 1990, 1991) to present an Ideal Performer Model.
      - vii. We do claim, however, that the outcome of this approach approximates what would be expected if human cognition calculated costs as if milliseconds mattered. Hence, a good fit of the model to the data will be taken as support for the soft constraints hypothesis and as evidence against the minimum memory hypothesis.
- - - - i. Participants
        
        Across each of the three studies a minimum of 16 and a maximum of 18 participants were assigned to each condition.
      - ii. Equipment and Software
        
        Macintosh computers
      - iii. Design
        
        a. Across all conditions of all experiments the Target, Resource, and Workspace windows were covered by gray boxes. Only one window was visible at any one time.
        
        b.Across the three studies, the only difference in procedure was in the method and cost of opening the Target window.
        
        c.Experiment 1. Three levels of access cost were varied.
        
        d. Experiment 2. To open the Target Window, all participants in Experiment 2 moved the cursor to a button located at the center of the Target window and clicked. In this experiment, the cost of accessing information was manipulated by changing the size of the button in the Target Window
        
        e. Changing the button size manipulated perceptual-motor effort along with time by changing the mean Fitts Index of Difficulty (MacKenzie, 1992) for moving to the button from either the Resource or Workspace window from 1.7 (e2-low) to 2.8 (e2-med) to 6.2 (e2 high).
        
        f. the Index of Difficulty can be considered a standard and generally accepted measure of the type of
        information access costs varied in this study.
        
        g. Experiment 3. For the third study, the buttons inside the Target Window were removed and the Blocks World display was restored to the look it had in Experiment 1
      - iv. Procedure
        
        To select a block, participants moved the mouse cursor to the Resource Window and clicked on a colored block.
    - - For each experiment, we provide one general measure of the differences between conditions and then focus on two specific measures
        
        The general measure is a count of the mean number of times during a trial that the Target Window was uncovered
        
        The two specific measures look at events surrounding the first uncovering of the Target Window: median duration of the first uncovering and mean number of correct placements following the first uncovering
        -There are two rationales for focusing on events surrounding the first uncovering
        
        First, for each trial, at the time of the first uncovering of the Target Window, there were eight not-yetplaced blocks. For all subsequent uncoverings, the mean number of not-yet-placed blocks varied between conditions. Comparing across conditions is easiest when the number not-yet-placed is equal for each condition
        
        Second, focusing on events prior to the second and subsequent uncoverings avoids any potential confound with any cumulative memory trace for the block pattern. This ensures that the measures of duration and correct placements can be attributed to events surrounding the first uncovering and are not influenced by a cumulative memory trace for the block pattern.
        
        i. Number of Target Window Accesses
        
        Each study showed a main effect of access cost condition on the
        mean number of times the target window was accessed
        
        ii. Duration of First Look
        
        Each study showed a main effect for condition on the median
        duration that the Target Window stayed open on its first access
        
        iii. Blocks Correctly Placed Following the First Look
        
        This measure examined the mean number of blocks placed after
        the first look that correctly matched the color and location of a
        block in the Target Window.
        
        iv. Discussion of the Experimental Data
        
        Each of the three studies found a progressive switch from more interaction-intensive to more memory-intensive strategies as information access costs increased
        
        The number of times the Target Window was opened decreased, while the duration that it was opened increased. Presumably, the increased duration that the Target Window was opened reflects increased time spent encoding its contents.
        
        This interpretation is supported by the increase in the number of blocks placed following the first look. As access costs increase, people minimize time per trial by accessing the Target Window less and using memory more
        
        v.Differences Between Methods of Information Access
        
        Across the three studies we varied the method of accessing the Target Window.
        
        If access costs are measured in time, then the Experiment 1 results are very regular.
        
        As access time increased, participants opened the Target Window less often, but the duration of the look increased, as did the number of correct and incorrect retrievals from memory.
        
        The Experiment 1 and 2 results suggested that, for the
        Blocks World task, time is the operative factor and it does not matter whether time for information access is manipulated by varying the Fitts Index of Difficulty or by lockout.
        
        The use of lockout time in Experiment 3 also enabled us to more precisely control access time while also producing a wider range of access costs.
        
        Hence, Experiment 3 provides our best empirical test of the notion that access costs can be measured by access time.
        
        Across three studies, the empirical data support the view that as access costs increased participants switched from more interaction-intensive to more memory-intensive strategies.
        
        This
        strategic switch was signaled by the decreasing number of openings of the Target Window across conditions as well as by the increasing duration that the Target Window was open
        
        We argue that the increase in the duration that the Target Window is open reflects the greater amount of time that participants spent encoding the contents of the Target Window
        
        This explanation is supported by the increase across conditions in the number of correct block placements following the initial uncovering of the Target Window.
        
        vi. Limits of the Experimental Data
        
        The empirical data demonstrate that as access costs increase people adjust their strategies to be less interaction intensive and more memory intensive
        
        However, although we view the steady increase in tradeoffs as persuasive evidence in support of the soft constraints hypothesis, the empirical data do not rule out weaker forms of the minimum memory hypothesis.
        
        For example, the soft constraints hypothesis argues that as information access costs increase, the use of interaction-intensive versus memory-intensive strategies is driven by their expected utility (i.e., cost-benefit tradeoff) as measured by time
        
        The empirical data show a shift in strategies but, by themselves, do not relate the shift to expected utility.
        
        As discussed in the next section, conformity to the reinforcement learning solution would support the soft constraints hypothesis. In contrast, deviations from the reinforcement learning solution would support the minimum memory hypothesis.
- - - - The goals of the human performer combined with the physical properties of the task environment act as hard constraints on how the task is performed
        
        Given the task environment shown in Figure 1 and the goal to reproduce the pattern of Target Window blocks in the Workspace Window, then the task analysis breaks the task into a series of ENCODE-k strategies where k is the number of blocks (1– 8) encoded on each round. Each ENCODE-k strategy consists of two unit tasks, an Encode Blocks unit task and a Get & Place unit task.
        
        For the Encode Blocks unit task the performer must shift visual attention to and move the mouse into the Target Window
        
        Between conditions, hard constraints built into the task environment determine how long the performer must wait until the window opens
        
        The second unit task is Get & Place. In this unit task the performer must move visual attention and the mouse cursor into the Resource Window (lines 11–12), which then opens.
    - - Within the cognitive task analysis defined by the pseudocode of Table 5, the column “cost (in ms)” defines known human limits, or side conditions, to each step.
        
        A key source of constraints imposed on the ideal performer is the memory limitations resulting from a fallible human memory
    - - consistently choosing the ENCODE-1 strategy corresponds to an extreme interaction-intensive strategy, while consistently choosing ENCODE-8 corresponds to an extreme memory-intensive strategy.
    - - Unfortunately, we cannot predict the sequence of state-action pairs used across the six conditions of Experiment 3 simply from knowing the task structure and human performance limits.
        
        In addition to these constraints, a numerical objective function must be specified for an ideal performer to maximize its achievement according to this function.
        
        A strict, literal interpretation of this hypothesis suggests only that the ideal performer seeks to minimize the burden on its memory system.
        
        A direct way to maximize this objective function would be by choosing the ENCODE-1 strategy on each round, regardless of lockout cost.
        
        In contrast, the soft constraints hypothesis makes a clear prediction regarding the objective function that should be maximized.
        
        If, as the soft constraints hypothesis assumes, the cognitive system is indifferent to the type of internal resources it exploits as well as to the location of the information it accesses (in-the-world vs. in-the-head) then it should simply maximize expected utility according to a cost-benefit tradeoff between competing interactive routines.
        
        Unfortunately, while specifying a suitable objective function is straightforward, maximizing achievement of the objective function to determine optimal performance is not an easy task.
        
        To some degree, humans have some metacognitive sense regarding how likely they are to remember something, given how much effort they are willing to spend memorizing it, and given the length of time they need to remember it.
        
        For example, when looking up a telephone number in a directory, the time spent committing the number to memory reflects a tradeoff between the time it must be held in memory and the time required to relocate the number if it is forgotten while walking across the room to the telephone.
        
        In general, there seem to be many life events when information is temporarily needed and we make a tradeoff between encoding effort, retention interval, and the cost of reacquiring information if we forget it.
    - - The final component of the ideal performer analysis is a formal mechanism for maximizing performance according to the objective function while simultaneously satisfying the constraints imposed by the human performer as well as the task itself.
        
        In our model we employed a reinforcement learning algorithm, Q-learning, that is formally guaranteed to converge on the optimal solution to this tradeoff if provided with sufficient training and adequate exploration of the problem space
        
        Reinforcement learning entails an unsupervised, trial-and-error exploration of the task environment, in which rewards can be defined in terms of minimizing solution time.
        
        In recent years researchers in the neurocognitive community have examined reinforcement learning as a plausible model of how humans learn from their mistakes
        
        However, for the purpose of this research we are interested in reinforcement learning not as a theory of human cognitive functioning, but rather as a tool for determining optimal performance by maximizing expected utility under a set of explicit constraints.
        
        Reinforcement learning has similarly been used to approximate optimal motor control in reaching tasks and as a model of motor learning
        
        In introducing the soft constraints hypothesis, we wrote of
        maximizing expected utility in terms of a cost-benefit tradeoff.
        
        In implementing the soft constraints hypothesis in a reinforcement learning approach, the outcomes of actions are defined only in terms of their local cost
        
        Benefit in the model is implicitly defined as minimizing global costs—that is, the time required to complete an entire trial.
        
        Hence, in the reinforcement learning model, just as costs are defined by time, benefits are defined as minimizing time. Optimizing benefits entails minimizing costs.
    - - The ideal performer analysis combined elements of a traditional ideal observer analysis (Geisler, 2003; Macmillan & Creelman, 2004) with a rational analysis (Anderson, 1990, 1991) to produce our Ideal Performer Model
        
        At the top level of description, the requirements of the model were defined by the goals of the task and the task environment
        
        Most of the times for cognitive, perceptual, and motor operations reflected accepted estimates for performance.
        
        The most notable limit we discussed was the time required to encode an item into memory, the time required to later retrieve that item, and the probability that retrieval would be successful.
        
        Our estimate of these times and probabilities are directly derived from Anderson’s rational analysis model of memory
        
        Performing the Blocks World task was defined as a series of choices among ENCODE-k strategies for each state of a Blocks World trial.
        
        Optimizing this series of choices by an objective function that minimizes total time (according to the soft constraints hypothesis) is a hard problem in large part due to the probabilistic nature of human memory
        
        As we lack a cognitively valid formal mechanism for maximizing achievement of this objective function, we turned to a reinforcement learning technique, Q-learning, that is formally guaranteed to find an optimal solution if certain assumptions are met
- - - - The challenge for the reinforcement-learning model is to extrapolate from local rewards following each ENCODE-k strategy to an estimate of the time required to complete an entire trial for each action and in each state.
        
        The output of the Ideal Performer Model consists of two sets of information.
        
        The first is the table of utility estimates for each state-action pair
        
        As such, the ability of the Ideal Performer Model to fit the human data provides a strong test of the claim that time cost acts as a soft constraint in the Blocks World task.
        
        The second piece of information produced by the Ideal Performer Model is the number of blocks successfully recalled and placed as a function of the number encoded in memory
        
        The memory equations involve three parameters: a retrieval threshold, an activation noise parameter, and a latency scaling parameter,
        
        Although the utility table defines the optimal strategy for the first visit to the target window (deterministically choose the strategy with the highest utility), we have theorized that time is a soft, as opposed to hard, constraint in the task.
        
        Consequently, we expect that participants will not always select the optimal strategy, but rather will approximate the optimal policy to the extent that their behavior is influenced by time as a soft constraint
        
        To transform a utility estimate into a selection probability, we used ACT-R’s strategy selection equation, the “softmax” rule, which has also been widely used in other reinforcement learning models
        
        Since utility in our model is defined strictly in terms of time, this allows us to determine the probability that our model will discriminate between two strategies with a given difference in expected time cost.
        
        The ideal performer analysis also makes predictions about two other empirical measures reported for the human participants.
        
        The mean duration of the first look to the target window is jointly determined by the estimated costs from the task analysis in Table 5 and the probability of selecting each ENCODE-k strategy.
        
        Finally, the expected number of visits to the target window can be determined using Monte Carlo simulation of the Ideal Performer Model
    - - The predictions of the Ideal Performer Model are dependent on
        four parameters (three parameters for the memory equations and one noise parameter for the strategy selection equation).
        
        It is worth repeating that the model’s predictions were fit to just one of the empirical measures (number of blocks placed, Figure 3), while the three remaining predictions—distribution of blocks placed (see Figure 4), number of visits to the target window (see Figure 6), and duration of first uncovering (see Figure 5)—all closely matched human performance using the same parameter settings.
    - - The results of the Ideal Performer Model across four empirical measures suggest that human performance on the Blocks World task reflects a cost-benefit tradeoff between perceptualmotor and memory costs defined by time.
        
        Within the constraints of memory and perceptual-motor limits, the human control system adapts to the costs of information access in its task environment by making rational, cost-benefit tradeoffs among sets of more interaction-intensive and more memory-intensive strategies.
        
        The Ideal Performer Model is not biased to favor perceptual-motor effort over memory effort. Rather, it is sensitive only to costs and benefits defined by time.
        
        Hence, the results support the soft constraint perspective on embodied cognition that views memory and perceptualmotor resources as allocated by a control system that attempts to optimize performance time
        
        It seems improbable that a computational model employing the minimum memory hypothesis would be able to account for the same broad range of results.
- - - - The Target Window stayed open for as long as the mouse cursor remained inside it (in E1-low—for as long as the control key was held down). The Resource Window and Workspace Window worked exactly the same across all studies and conditions; both opened as soon as the mouse cursor entered and stayed open until the mouse cursor left.
        
        Another way of saying this is that once the Target Window opened, the task was exactly the same across all conditions and all studies, and no hard constraints existed that would account for why the task was not performed exactly the same
        
        However, for the current studies, even when the comparisons between two conditions were not significant (e.g., as for e1-low vs. e1-med) an increase in the range of 50 ms to uncover the Target Window resulted in small, but consistent, increases in the duration for which the Target Window was uncovered and small, but consistent, increases in the number of blocks placed.
    - - between access costs and the use of more interaction-intensive or more memory-intensive strategies, the studies did not suffice to determine the nature of that tradeoff
        
        To precisely predict what an optimal tradeoff would be between perceptual-motor and memory costs, we created an Ideal Performer Model that maximized performance in the Blocks World task by selecting ENCODE-k strategies that minimized the total expected time to complete each trial for each of the six between-subjects conditions of Experiment 3.
        
        The Ideal Performer Model used realistic assumptions regarding the time required to execute each interactive routine. For memory operations it used a memory model, based on rational analysis, that yielded assumptions about encoding duration, retrieval latency,and the forgetting that would occur in the retention interval between encoding and placement
        
        We conclude that, subject to the limitations of the memory system, human performance is nearly identical to what would be expected if the allocation of cognitive, perceptual, and motor resources was based on their temporal costs and if overall benefit was defined by minimizing these costs.
        
        Cost-benefit tradeoffs among lockout time, perceptual-motor activity, and fallible memory act as soft constraints that select the interactive behaviors that are best adapted to the task environment.
    - - The success of the model has implication for theories of memory.
        
        First, it shows that a model based on a rational analysis of the demands the environment makes on memory can be successfully applied as a constraint on a rational analysis of interactive behavior
        
        Second, regardless of the ultimate validity of Anderson’s model of memory, its use in the Ideal Performer Model provides a strong suggestion for the form in which theories of memory must take if they are to be usefully applied to interactive behavior
        
        Rather than simply focusing on the number of slots or amount of activation, the Ideal Performer Model suggests that theories of memory must encompass three additional factors.
        
        First, is the time needed to raise the activation of an item so that it can be retrieved over the time period for which the item is needed
        
        Second, is the time required to retrieve an item from memory
        
        Third, is the probability that an encoded item will be retrieved due to decay and noise in the item’s activation.
        
        Additionally, the close fit of the human data to the predictions of the Ideal Performer Model suggests that people have implicit knowledge or metacognition of these three memory factors, and, with relatively little experience with a new task (within 10 trials in our studies), are able to near-optimally adapt their interactive behaviors to meet the demands of the task environment.
    - - For example, the soft constraints hypothesis addresses two claims in Wilson’s (2002) taxonomy of embodied cognition
        
        First, is the claim that we off-load cognitive work onto the environment.
        
        Second, is the claim that the environment is part of the cognitive system.
        
        The power of the Ideal Performer Model flows directly from our combination of an ideal observer analysis with rational analysis.
        
        The Ideal Performer Model shows that a rational analysis of one side condition, in this case human memory, can provide an important bound that allows us to make progress on a rational analysis of another side condition, in this case, optimizing the use of internal resources by cost-benefit tradeoffs in the access of knowledge in-the-world versus in-the-head.